Technically Exists

All airs ache

2026-04-01T00:00:00+00:00

All airs ache.

Blue burns bright.

Cats catch crags.

Dust drains dry.

Elms end ebbs.

Fear fights friends.

Ground grinds gold.

Help holds halls.

Inns ice ill.

Joints jump junk.

Kills kick kegs.

Lips last long.

Mines mash maws.

Nil nears next.

Odds owe out.

Pulls push past.

Qualms quip quests.

Rice rips racks.

Some stars stir.

Tubs tuck trucks.

Urns use ups.

Veins vault views.

Weeks will wisps.

Xysts X xi.

Yaw yells yaks.

Zilch zips zoos.

Time is valuable

2025-04-01T00:00:00+00:00

Time is valuable. We all know this. And since the technology required to instantaneously consume blog posts has yet to be invented, you must spend some of your valuable time in order to read this blog. As such, it is important that I get to my points quickly and keep my posts as short as reasonably possible.

Thank you for reading!

Cooperation in the one-shot prisoner's dilemma

2024-04-14T00:00:00+00:00

One of the most important scenarios in game theory is the prisoner’s dilemma. In this scenario, two criminals are arrested after working together. The police don’t have enough evidence to get the criminals convicted of every charge, but there is a charge for which they do have enough evidence to get a conviction. Thus, the police decide to offer the prisoners a choice. They can either confess to their crimes or remain silent. If both confess, they each receive 2 years in jail. If one confesses and one remains silent, the confessor receives no jail time and the silent prisoner receives 3 years in jail. If both prisoners remain silent, they each receive 1 year in jail. You can see this displayed in the table below.

	Prisoner B remains silent	Prisoner B confesses
Prisoner A remains silent	A: 1 year B: 1 year	A: 3 years B: 0 years
Prisoner A confesses	A: 0 years B: 3 years	A: 2 years B: 2 years

We can abstract this scenario by converting the years served in jail into utilities¹, replacing confessing with the action “cooperate” and remaining silent with the action “defect”, and replacing the prisoners with agents A and B.

	Agent B cooperates	Agent B defects
Agent A cooperates	A: 2 B: 2	A: 0 B: 3
Agent A defects	A: 3 B: 0	A: 1 B: 1

There are two important facts about this table. The first important fact is that mutual cooperation is better for both agents than mutual defection. The second important fact is that, regardless of what agent B chooses, agent A is always better off defecting, and vice versa. If one agent chooses to cooperate, the other gains 3 utils by defecting and only 2 utils by cooperating. If the first agent instead chooses to defect, the other agent gains 1 util by defecting and 0 utils by cooperating. Thus, it seems like a rational agent playing this game should always defect.

The decision theory used to justify this reasoning is called causal decision theory (CDT), and it is the widely-accepted standard for rational decision-making. CDT states that an agent should choose the action that will cause the best outcome in expectation, which sounds very reasonable. But CDT has some problems. In the case of the prisoner’s dilemma, a pair of CDT agents will predictably do worse than a pair of agents that manages to achieve mutual cooperation. Thus, an interesting problem is to figure out what strategies agents can use, if any, to achieve mutual cooperation.

Unsurprisingly, a lot has been written on how to obtain mutual cooperation in the prisoner’s dilemma. A popular approach is to consider the iterated prisoner’s dilemma, where agents play each other multiple times in a row with knowledge of the actions taken in previous rounds. However, this post will only consider instances of the one-shot prisoner’s dilemma, where two agents play each other once and never interact again. One instance of the one-shot prisoner’s dilemma is the psychological twin prisoner’s dilemma. This scenario is designed to make mutual cooperation in the one-shot prisoner’s dilemma as easy and tempting as possible, as it specifies that the agents are psychological twins in identical scenarios that will therefore always behave exactly the same. It also specifies that both agents know this, so they can take it into account when making their decision.

There are only two possible outcomes in this scenario; either both agents cooperate or both agents defect. It seems like this change should make cooperation the rational answer, but there’s a catch. There is no causal link between the agents’ decisions. Instead, their identical behavior arises from a logical dependency. Because of this, CDT continues to recommend defection in this scenario. Fortunately, there are alternatives that recommend cooperation instead, though to understand the differences between them we will have to look at more scenarios than just the prisoner’s dilemma.

One of these proposed alternatives is the notion of superrationality. A superrational agent mostly reasons the same way as a CDT agent, but they also recognize that other superrational agents will reason the same way as they themself will. Thus, a superrational agent will take into account the logical dependency introduced in the psychological twin prisoner’s dilemma and choose to cooperate with their twin. However, superrationality does not take into account all logical dependencies.

Consider the case of Newcomb’s problem. In this scenario, a trustworthy and accurate predictor known as Omega sets up a game with two boxes. Box A is transparent and contains $1,000. Box B is opaque and contains either $1 million or nothing. An agent is given the option to take both boxes (two-box) or to just take box B (one-box). The trick is that before the agent chooses, Omega predicts their decision and fills box B if and only if the agent will one-box. Thus, an agent that two-boxes will end up with only $1,000, while an agent that one-boxes will end up with $1 million. However, the presence or absence of the $1 million is not caused by the agent’s decision, but rather by Omega’s prediction of the agent’s decision. This means that CDT recommends two-boxing. Superrationality will do the same, even if Omega is known to be superrational. This occurs because Newcomb’s problem is asymmetric; Omega is faced with a completely different decision (whether or not to fill box B) than the agent is (whether or not to take box A in addition to box B).

Superrationality is not the only alternative to CDT, nor is it the most prominent. CDT’s main rival is actually something called evidential decision theory (EDT). EDT states that an agent should choose the action that will, upon the agent learning that they have taken that action, be evidence of receiving the best outcome in expectation. In other words, an EDT agent considers whether or not it would be good news to learn that they had taken a particular action.

This way of reasoning allows the EDT agent to take into account logical dependencies like those introduced in the psychological twin prisoner’s dilemma and Newcomb’s problem. Thus, an EDT agent in those scenarios will choose to cooperate with their twin and one-box, respectively. Unfortunately, this nice behavior comes at a cost. EDT agents take into account all statistical correlations, and not all correlations correspond to causal dependencies or logical dependencies.

An example that demonstrates this is the XOR blackmail scenario. In this scenario, an agent learns of a rumor that their house might be infested with termites. If this is true, then they will have to pay $1 million in order to remove the infestation and repair the house. A trustworthy and accurate predictor has investigated whether or not this claim is true. This predictor then decides whether or not to send a letter to the agent asking for $1,000, but they make this decision in a unique way. Specifically, the predictor sends the letter if and only if one of the following is true.

The agent’s house has termites, and the predictor predicts that the agent won’t send them $1,000 upon receiving the letter.
The agent’s house does not have termites, and the predictor predicts that the agent will send them $1,000 upon receiving the letter.

The letter also contains an explanation of the above, so the agent knows that either 1 or 2 is true. Upon receiving the letter, a CDT agent notices that choosing to pay the $1,000 will not cause a termite infestation to disappear, and therefore decides not to pay the $1,000. A superrational agent will reason the same way, even if they believe the predictor to also be a superrational agent. However, an EDT agent will reason that it would be good news to learn that they had paid the $1,000, since this would indicate that there is no termite infestation and they don’t have to pay $1 million to remove it. Thus, an EDT agent does decide to pay the $1,000. This makes the EDT agent a target for any blackmailer who can set up a similar scenario.

Is there a decision theory that can generalize the behavior of superrationality by taking into account logical dependencies like those in the psychological twin prisoner’s dilemma and Newcomb’s problem, but not purely statistical dependencies like the one in XOR blackmail? Logical decision theories are a family of decision theories that attempt to do so.

One example of a logical decision theory is proof-based decision theory, which arose from work done in Robust Cooperation in the Prisoner’s Dilemma: Program Equilibrium via Provability Logic. This paper constructed an agent called FairBot, which when given the source code of the bot that it is playing against, cooperates if it can prove that its opponent cooperates when given FairBot’s source code. Thanks to the existence of Löb’s theorem², FairBot actually will cooperate with itself without getting stuck in a loop of self-reference! At the same time, FairBot will never allow itself to be exploited by cooperating with an opponent that will defect against it.

The same paper went on to construct a second agent that will cooperate with itself called PrudentBot. PrudentBot behaves similarly to FairBot and will always defect when its opponent defects. In addition, it will choose to defect when up against an agent that always cooperates³, unlike FairBot which cooperates in that scenario and thus loses utility. Even more impressively, FairBot and PrudentBot will actually cooperate with each other, indicating that mutual cooperation can go beyond situations in which the agents reason identically. Proof-based decision theory does come with some serious limitations, the most obvious being that it can only reason about agents properly when it has access to and can prove statements about their source code.

A logical decision theory that lacks this limitation is functional decision theory (FDT). FDT states that an agent should choose the action that, when output by all instances of their decision function, causes the best outcome in expectation. An FDT agent will thus consider not just the effects of themself making a decision, but also the effects of other agents that reason like them making the same decision (like their psychological twin), the effects of other agents predicting that they will make the same decision (like Omega and the XOR blackmail predictor)⁴, and the effects of their decision in any other situation in which an instance of that decision occurs.

In the psychological twin prisoner’s dilemma, an FDT agent recognizes that their twin uses the same decision function as themself and thus cooperates, knowing that their twin will also cooperate. In Newcomb’s problem, an FDT agent recognizes that their decision function controls whether or not box B is filled via Omega’s prediction, and thus one-boxes in order to receive $1 million. In XOR blackmail, an FDT agent recognizes that their decision function is one of the factors controlling the predictor’s decision, but the agent also recognizes that their decision function has no influence over whether or not termites are present, and thus does not send $1,000 upon receiving the letter.

Not only can FDT outperform CDT in some scenarios and EDT in others, it can sometimes outperform both in the same scenario. Parfit’s hitchhiker falls into this category. In this scenario, a selfish driver comes across an agent stranded in the desert. The driver offers to take the agent to the nearest city, but only if the agent will pay them $1,000. The agent does not have $1,000 on them, but they can withdraw $1,000 from an ATM in the city. The driver is an expert at using facial microexpressions to detect lies, and so they ask the agent whether or not they will pay $1,000 upon arriving in the city. If the agent refuses or lies, the driver leaves them to die in the desert. Otherwise, the driver brings them to the nearest city.

In this scenario, the decision is whether or not to pay the $1,000 once in the city. A CDT agent reasons that paying the $1,000 will not cause them to be rescued because they already have been rescued, and thus refuses to pay. A superrational agent reasons similarly, even if the driver is also superrational. An EDT agent reasons that since they have already been rescued, learning that they had paid $1,000 would be bad news since that just means they have lost $1,000. Thus, all of these agents end up dead in the desert.

An FDT agent that values their own life more than $1,000 reasons differently. They recognize that their decision function controls not just their actual decision, but also their own prediction of their decision. They also know that this prediction will affect their microexpressions in a way that determines whether the driver will believe them if they say they will pay. Thus, the agent will decide to pay up once in the city, ensuring that they are rescued.

FDT is very good at achieving the best possible outcomes in various scenarios. However, it does have a major shortcoming at the time of writing. It relies on a model of logical and causal dependencies in order to make its decisions, but as of now there is no fully general method for producing these models. In contrast, there is a known method for producing the purely causal model used by CDT. Whether or not an analogous method is found for FDT could be the difference between it eventually replacing CDT as the standard for rational decision-making or fading into obscurity.

For this example, I used $u = 3 - y$ for the conversion, but this is somewhat arbitrary. ↩
If you’re interested in learning about Löb’s theorem and hate mathematical notation, I highly recommend reading The Cartoon Guide to Löb’s Theorem. ↩
It is arguably the case that an agent which always cooperates is less like an actual agent and more like a sign with the word “cooperate” written on it. Thus, there is no advantage to rewarding it with cooperation. ↩
This post will assume that all predictions are made based on the agent’s decision function and its consequences. It is possible to create scenarios in which predictions can be made with high accuracy based on factors not influenced by the agent’s decision function, such as an agent’s date of birth. In this case, the prediction takes advantage of an existing statistical correlation without creating a logical dependency, which can change the behavior of logical decision theories. ↩

Looking back

2024-04-01T00:00:00+00:00

Over the past 7 years I’ve written 39 posts on this blog, not including this one. Some of them I’m really proud of. Others, not so much. I figured it might be nice to give readers some insight into how I view my previous work, so I’ve split my posts into three categories, along with a brief justification for each post’s categorization.

This now exists: Meh. Would’ve been nicer if Video game boycotts was my first post, but it’s not like this one is particularly bad.

Video game boycotts: Based. My urge to write up this post (and the next) was what motivated me to create this blog, and I’m very happy with how well it’s held up.

Can boycotts be solved?: Based. I think I do a good job of covering a couple non-obvious options, and would be really interested to see if someone could get something based on the Kickstarter-like boycott company to work.

Colonizing Mars does not mean abandoning Earth: Meh. There’s nothing really wrong with this post, but it was written back when I thought colonizing multiple planets was one of the better approaches to managing existential risk, whereas I now believe it does nothing to help with what is by far the largest such risk.

Singletons and universal inevitable threats: Meh. I think the concept is worth having, but the name is a bit of a mouthful, and the motivating factor was arguably just a nitpick.

How intelligent are we?: Cringe. I think this just ended up as a restatement of some arguments made in Superintelligence: Paths, Dangers, Strategies.

Arguing over definitions: Meh. I kind of want to write about a related topic, but this post doesn’t seem good enough to bother building off of.

How to win The Game: Based. I am very proud of outsmarting The Game’s inventor, and I highly recommend reading this post if you know what The Game is and aren’t satisfied by xkcd 391.

Comic Sans is a great font: Cringe. Comic Sans is awful and I don’t know what I was thinking.

Freedom of speech is bad: Cringe. I had this concept of splitting up arguments for and against certain ideas into two separate posts, and it didn’t really make sense.

Freedom of speech is good: Cringe. I can’t be too upset with my past self for experimenting like this, but ultimately it made these posts awkward, which is a shame because they were some of the first to actually see engagement.

Outlining the opposite of a singleton: Meh. I originally planned to follow up with a post giving examples of replicator worlds but never did, and without any examples, this post is just oddly abstract.

My thoughts on Microsoft acquiring GitHub: Based. As far as I know, no one seems to think that GitHub is worse than before the acquisition, and I still dislike the consolidation of market power that these deals tend to lead to.

Why discuss superintelligence?: Based. This post mostly just existed to introduce the Superintelligence reference page, which I should probably start updating again now that LLMs are taking off.

Should you pursue common or rare achievements?: Based. This post is kind of silly and very much based on personal preference, but the reasoning holds up well in my opinion.

STAR voting in an interstate compact: Meh. This is a fairly nice proposal, but it does make some awkward compromises, and it’s not really relevant to actual reform efforts.

Ranked choice voting is worth supporting: Cringe. I really should have written about STV here, defending IRV is a lot harder since it still struggles with the core problem of vote-splitting.

The world’s problems: Based. The post ranks the problems that I considered most important which is kind of cringe, but I think this is outweighed by how well it identified important problems, even though their relative importance might be a bit off.

On normative ethical theories: Cringe. The core premise of this post is wrong since the von Neumann-Morgenstern utility theorem requires utility to be bounded while utilitarianism requires unbounded utilities.

The meaning of one person, one vote: Based. People sometimes talk past each other when it comes to one person, one vote, and I think this post did a good idea of clarifying the different interpretations being used.

Thanos is a straw centrist: Meh. I probably could’ve put more effort into this one, but I did enjoy drawing a link between straw centrism and sortition-powered mass murder.

Why 1 is not prime: Based. I remember being really frustrated when various sources explaining why 1 isn’t prime would just mention the Fundamental Theorem of Arithmetic and call it a day (as if you couldn’t alter the theorem more easily than the definition of primes), so I am really happy to have written up several more examples where 1 doesn’t follow the pattern for primes.

Soul harvester: Meh. This is another experimental post and one which I’m fond of, but it once again ends up feeling awkward, like I should have just written a normal short story instead.

Quadratic voting and types of one person, one vote: Based. This post does a good job of introducing formalizations for the concepts being discussed, and it demonstrates the differences between these concepts in a pleasing way by making successive modifications to quadratic voting.

The NPVIC, RCV-1, and Maine: Based. The NPVIC advocates and the RCV advocates tend to get along well, so it’s worth highlighting that they really should have a more concrete plan.

The motivation behind SPSV, part 1: Meh. This is a very brief introduction to the difference between bloc voting methods and proportional voting methods and doesn’t really stand on its own, but it’s alright as the first post in a series.

The motivation behind SPSV, part 2: Based. This post actually deals with a specific voting method, allowing it to be more fleshed out.

The motivation behind SPSV, part 3: Meh. This post introduces a party-agnostic proportional voting method and does a good job of comparing it to the voting method from the previous post, but it doesn’t actually give an example of how this new method generalizes better.

The motivation behind SPSV, part 4: Based. This post does a good job explaining the reweighting formula for RRV.

The motivation behind SPSV, part 5: Based. This is the most detailed post in the series and it benefits from this, covering everything from the KP transform to ternary plots for proportional voting methods.

Social choice theory paradigms: Based. A short but effective defense of favoring probabilistic analysis over pass/fail analysis.

On dealbreaker voting criteria: Based. I think there’s a need to think a lot more carefully about when and how to emphasize certain criteria in the course of advocacy in order to avoid being hypocritical, and this post does a good job getting at that.

Combining anarcho-primitivism and transhumanism: Based. I am very proud of combining two ideologies generally considered to be opposites into a coherent and even somewhat desirable alternative.

Why I like STAR voting: simplicity and familiarity: Based. This post makes the case that STAR voting isn’t all that complex, and I think it succeeds at this.

Why I like STAR voting: the 5-star ballot: Based. I am a huge fan of rated ballots, and I think I did a good job of making a case for them as part of the case for STAR voting that could also be viewed as an argument independent of any particular rated voting method.

Why I like STAR voting: pre-election polls: Based. The Center for Election Science does a good job of covering the advantages of approval polls, but the Equal Vote Coalition generally neglects the potential advantages of STAR polls, and this post helps to fill in that gap.

Why I like STAR voting: BRANDING: Cringe. This post suffers from a huge amount of awkwardness, and does a disservice to the topic of STAR’s branding.

Why I like STAR voting: winner selection: Based. This is the core reason why STAR voting is a good voting method, and this post does an excellent job of covering STAR voting’s accuracy in depth while also mentioning the majoritarian perspective.

An apology: Cringe. Some of these posts may have deserved apologies, but most of them did not, and many of the apologies are made for the wrong reasons.

In total, I’ve written 8 cringe posts, 10 meh posts, and 21 based posts, or 22 if you include this one. It seems like the average quality of my posts has improved over time; the first half of my posts includes 8 based posts and 6 cringe posts, while the second half includes 14 based posts and only 2 cringe posts. Hopefully I can continue to improve and bring you higher-quality content.

An apology

2023-04-01T00:00:00+00:00

I’m writing this post today to apologize for my past behavior. Ever since this blog existed, I’ve published an April Fools’ Day post each year about some topic or other that wasn’t meant to be taken seriously. However, it has been brought to my attention that not only do these posts fail to be humorous, they also degrade the seriousness of both the topics they cover and the blogosphere as a whole, in a way that can be quite dangerous.

Take, for example, On normative ethical theories. This post touches on a very serious philosophical topic, but its content is one gag applied repeatedly to different ethical theories to supposedly convert them into the dangerous position known as utilitarianism. In reality, this gag effectively ignored all but one aspect of these ethical theories in order to hide their obvious superiority behind silly revisions, thus promoting the insidious utilitarian position in their place.

While this was the most egregious example, it is not the only one. Comic Sans is a great font uplifts a horrible scourge of a font using faulty argumentation and attacks on respectable groups. It paints its recognizability as a strength rather than the source of its infamy, it tries to trick people into using it for formal documentation by bringing up a flawed understanding of countersignaling, and it suggests that hard-working graphic designers are really snobbish elites who hate any design work not done by them, regardless of how good it is. The last of these in particular is a major accusation that should not be made even in jest.

Thanos is a straw centrist is another example of the dangers posed by these posts. It implies that centrism is simply a straw man position held only by comic book villains. However, centrists are real, and in the face of rising extremist threats to democracy, supporting the status quo is entirely unacceptable. These centrists need to realize that by not choosing a side, they are really supporting the downfall of our democratic system of governance.

The post Combining anarcho-primitivism and transhumanism is perhaps the most unique example, because it establishes a new ideology that is half-based on reasonable principles. Unfortunately, the other half is based off of transhumanism, a radical ideology that seeks to ingrain technology into every aspect of human existence. It completely lacks respect for nature and its bountiful gifts, as well as basic human dignity. Furthermore, by extending the reach of technology and thus electronic surveillance, it threatens to eliminate all remaining privacy and empower totalitarian governments. Instead of stepping deeper into the technological hellscape of today, we need to turn back the clock and revert to a simpler way of life.

Finally, we have Why I like STAR voting: BRANDING. This post is not especially bad in and of itself¹, but in context it is one of the more damaging posts. See, this post was released in the middle of my series on, well, why I like STAR voting. Improving the voting methods we use is one of the top 5 most important problems, so we cannot afford any humor when it comes to this topic. But even worse, this post presents itself as part of the STAR voting series, and thus directly undermines the rest of the posts in that series.

By writing all of these posts, I decreased the perceived seriousness of the blogosphere as a whole, hurting the reputation of a valuable medium. Given that there was essentially no upside to writing these unfunny posts, I clearly owe an apology to all of my fellow bloggers. But I also owe an apology to all of my readers who were subjected to these awful posts. And finally, I owe an apology to society as a whole for downplaying serious threats for the sake of my attempts at humor. I hope that I can do better in the future.

Some of the jokes are quite awful though. Like, was “The Borda count? More like, the boredom mounts!” really the best I had? And the BRANDING acronym is pretty pathetic too. ↩

Why I like STAR voting: winner selection

2023-03-30T00:00:00+00:00

This blog post is the fourth in a series of posts about STAR voting. If you haven’t read the previous entries, I recommend you start with the first entry before reading this one.

Previously I explained the importance of pre-election polls and the advantages that STAR polls have over other types of polls. I mentioned at the end that many of the properties that make STAR a good method for polling also make it a good method for choosing winners, and in this post I will justify the claim that STAR voting picks good winners. But first, we’ll have to discuss what it even means for a winner to be good in the context of single-winner elections. There are two major schools of thought on this, majoritarianism and utilitarianism, and I will start with the former.

Majoritarianism says that a candidate is good if they are preferred by over half of the voters, i.e. if they have majority support. This sounds pretty straightforward until you consider just what it means to be supported by a voter. Does being supported mean being that voter’s first choice? If so, then it’s impossible to guarantee a majority winner, and most competitive elections with more than two candidates—the elections where the choice of voting method matters most—won’t have a majority winner. Thus, most majoritarians turn to the notion of a pairwise majority instead.

A pairwise majority occurs when a majority of voters would prefer one candidate over another in a head-to-head election. This means that you can guarantee a pairwise majority by first eliminating all but two candidates, then holding an election just between those two remaining candidates. Well, almost. See, it’s also possible for a voter to be indifferent between the two candidates, which means you could have an election where, say, 49% of voters prefer the first candidate, 48% prefer the second candidate, and the remaining 3% are indifferent between the two. Thus, the type of majority that can be guaranteed is a pairwise majority among the voters who express a preference between the two candidates.¹

Since this is the case, you may be unsurprised to learn that this is the type of majority people mean when they say that a voting method “guarantees a majority winner”. For example, a top two runoff system first eliminates all but two candidates, then picks the candidate supported by a majority of the voters who showed up to express a preference between the two candidates in the second round. Voters who show up to the first round but not the second aren’t counted as part of the group from which majority support must be earned, and neither are voters who do show up but choose to vote for a write-in candidate (which is still allowed in many runoffs).

Single-winner ranked choice voting has the same type of guarantee. This method elects a candidate once they have majority support, but that majority is found via candidate elimination rounds, and it only considers the ballots that expressed a preference between the non-eliminated candidates. If all the candidates that were ranked on a given ballot have been eliminated, that ballot is exhausted and no longer counts as part of the group the majority must come from.

Thanks to the automatic runoff, STAR voting can also ensure that the winner has this type of majority support. In fact, it does this explicitly. STAR counts every ballot as either a vote for the first finalist, a vote for the second finalist, or a vote of no preference; the winner is the finalist with a majority of the ballots that were not votes of no preference, which is exactly the type of majority that can be guaranteed.

Personally, I am not much of a majoritarian. I find utilitarianism to be much more compelling. Utilitarianism essentially states that the best candidate is the one with the most total support, or equivalently, the greatest average support. Unlike majoritarianism, this takes into account the strength of voters’ preferences. A classic demonstration of this difference is the pizza scenario.

Suppose you and a pair of friends are looking to order a pizza. You, and one friend, really like mushrooms, and prefer them over all other vegetable options, but you both also really, really like pepperoni. Your other friend also really likes mushrooms, and prefers them over all other options, but they’re also vegetarian. What one topping should you get?

Majoritarianism answers with pepperoni and justifies this decision by pointing out that 2 out of 3 people prefer it to mushrooms. On the other hand, utilitarianism notices that those 2 people only have a weak preference for pepperoni while the 3rd has a very strong preference for mushrooms, and so it answers with mushrooms. Multiple surveys have shown that under this scenario, most people will choose to side with utilitarianism.² The main argument in favor of ignoring the intuition this scenario reveals is that it occurs in a context that is very different from politics. The counterargument is that creating a scenario in a political context biases people who have been taught that “democracy” and “majority rule” are synonymous but would otherwise favor utilitarianism.

The debate between majoritarianism and utilitarianism goes much deeper than this, but I won’t dive into it any further. If you’re interested in reading in-depth arguments for favoring utilitarianism over majoritarianism, you can start with this paper or this web page (you may need to reload the page a few times to get some of the larger gifs to load).

As an added bonus, a utilitarian winner will always exist, unlike a first-choice majority winner. Furthermore, multiple utilitarian winners can only ever exist if there is an exact tie for total support, which becomes incredibly rare as voters’ preferences are measured more precisely. This means that unlike with pairwise majority winners, we are nearly guaranteed to have exactly one utilitarian winner.

Alright, so that’s nice and all, but how do you tell whether a voting method is utilitarian or not? Well, you don’t. Or at least, you don’t divide voting methods into a binary set of categories like utilitarian and non-utilitarian. Instead, you measure how well voting methods perform on expected utility metrics. In other words, you figure out on average how much satisfaction each voter receives from the winners elected by each voting method over a bunch of elections. This can be accomplished through the use of computer simulations.

An election simulation starts by generating the candidates and electorate. Each voter in the electorate will have some set of preferences over the candidates. In most simulations, these preferences are generated by placing the candidates and voters in a multi-dimensional political space and assigning each voter more favorable preferences for the candidates located closest to them. These voters will then cast ballots, and the voting method being assessed is used to pick the winning candidate. Finally, the average satisfaction of the electorate is calculated and recorded.

Ok, why use simulations? By far the biggest reason for this is the lack of real-world data for almost all voting methods. Unfortunately, in order to acquire a sufficient amount of real-world data, you need to already have the voting method widely implemented. This means that the initial decision to implement a voting method can only be made based on simulated data. In fact, these decisions have historically been made without any data at all, which means that simply by running simulations we put ourselves in a position to make much better decisions than have been made in the past. The other reason to favor simulations is that unlike in real life, you can “read the minds” of the electorate, so you have perfect knowledge of their true preferences. In real elections, you have to resort to collecting polling data, which inevitably introduces some noise into the results, though it may not be much.

Now this is great and all, but there is a significant downside to relying on simulations: they may just completely fail to correspond to reality. Reality is complex, and voter behavior is especially complex. Does a simple spatial model in which voters have perfectly coherent preferences over all candidates and perfect knowledge of those preferences really capture the behavior of human voters? Well, probably not. But simulations can still be useful if their results are treated correctly. The simplest option is to treat a voting method’s performance in simulations as an upper bound on its real-world performance. After all, it’s pretty unlikely that the complications introduced by reality will just so happen to line up in the exact way needed to improve a voting method’s accuracy. In this way, simulations can be used to rule out voting methods with low accuracy, but they won’t confirm that voting methods with high simulated accuracy will perform well if implemented in our elections.

However, we can actually do a bit better than the upper bound approach here. See, many different people have ran many different simulations that were implemented in many different ways using many different assumptions. This gives us an opportunity to learn something about how well a voting method’s good performance will generalize across different models of elections. If a voting method is robust to many changes made across simulation models, it has a much greater chance of performing well under a model that actually does correspond to reality. Because of this, we’ll want to look at multiple sets of simulations.

The first set of voting method simulations I’ll cover is Warren D. Smith’s Bayesian Regret simulations. This is one of the most well-known sets of simulations out there, and it’s especially useful for our purposes because Smith varied many of the assumptions made in his models in order to ensure that the results weren’t too sensitive to any of them. There is, however, one small problem. These simulations are from 2000, but STAR voting wasn’t invented until 2014, so it isn’t included in the results. Luckily, there is a workaround. Warren Smith may not have been able to simulate STAR, but he was able to simulate score voting with a manual top-two runoff. While these two methods have different strategies associated with them, they behave essentially identically under honesty. Thus, while we can’t really make use of the results from simulations with strategy, we can learn something about how well STAR performs with honest voters.

So how well does STAR perform according to these simulations? The answer is very well. With 13 honest voters, score voting with a top-two runoff (labelled Range2Runoff on the page) has a Bayesian Regret value of 0.121. In contrast, approval voting had a value of 0.190, ranked choice voting (labelled IRV) had a value of 0.217, and plurality/FPTP had a value of 0.331. (Do note that since this is a measure of regret, lower numbers are better. A value of 0 means the best winner was picked every time, and if the worst winner was picked every time that would, in this case, correspond to a value just over 2.) It also beats many other sophisticated voting methods like ranked pairs and Schulze. Overall, the regret from this method is the 8th lowest out of the roughly 50 voting methods that were tested in these simulations.

Next, we’ll take a look at Jameson Quinn’s Voter Satisfaction Efficiency simulations.³ This is another well-known set of voting method simulations, and similar to what Warren Smith did, Quinn made sure to vary many of the assumptions that his model made. Unlike the previous set of simulations however, these ones make use of a more realistic hierarchical clusters model. They were also ran in 2017, which means they were able to include STAR voting explicitly. This means that this set of simulations gives results for both honest voters and strategic voters.

The results for this simulation are reported using Voter Satisfaction Efficiency (VSE), a metric which I’ve covered before. A VSE of 100% corresponds to always picking the best winner, and a VSE of 0% corresponds to picking a winner uniformly at random. Looking at the results for STAR voting with a 5-star ballot, under honest voting STAR has a VSE of 97.7%. When half the electorate votes strategically it only drops to 97.3%, and when the entire electorate votes strategically it drops to 94.1%. The worst-case scenario occurs when the dominant faction votes honestly while the underdog faction votes strategically, and even then VSE only falls to 90.9%.

In comparison, approval voting’s VSEs fall in the range 84.1%-95.5%, ranked choice voting’s in the range 79.7%-91.3%, and plurality/FPTP’s in the range 71.8-86.0%. The only scenario in which approval voting outperforms STAR voting is when all voters are strategic. There is no scenario in which ranked choice voting outperforms STAR voting, and plurality voting actually performs worse in every scenario than STAR’s worst-case performance. Once again, STAR voting proves itself to be more accurate than a variety of alternatives. The only voting method tested that was able to more-or-less match STAR’s performance was 3-2-1 voting, which like STAR voting is a rated runoff method. Compared to STAR’s VSE range of 90.9%-97.7%, 3-2-1’s range was 91.9%-95.1%.

The last set of simulations I’ll discuss are John Huang’s Voter Regret and VSE simulations. These simulations are from 2020 and 2021, making them more recent than most. They are divided into 3 sets, which all make use of various spatial models. Both the first set and second set only consider honest voters, while the third set introduces 2 kinds of strategy. Rather than going through each of these individually, I’ll give an overview of the summary report, which primarily relies on the results from the third set. That being said, I do recommend taking the time to check out all 3 sets of results.

As with Quinn’s simulations, the results are reported in terms of VSE. STAR voting has an average VSE of 85.8%, which is second only to Smith//Score’s average VSE of 87.0%.⁴ Approval voting’s average VSE is 77.2%, ranked choice voting’s is 72.5%, and plurality/FPTP’s is a measly 51.5%. Based on these results, the executive summary states that:

This report ultimately finds that several methods have excellent performance in their ability to choose candidates which satisfy a greater number of voters than other methods. These best methods include Condorcet-compliant methods, STAR voting, and Smith-Score. Among the highest performing methods, STAR voting is the simplest to implement and compute.

The results section reiterates this recommendation:

Based on these results, I recommend the replacement of plurality voting with any of the above tested voting methods, all of which are superior to plurality in the scenarios tested. However for optimal results, I recommend STAR voting or Condorcet methods.

All of these simulations indicate that STAR voting is a highly accurate method on par with sophisticated methods such as Condorcet methods and 3-2-1 voting. While none of them are able to capture reality in all its complexity, their results indicate that STAR voting’s strong performance should generalize to most situations, including most that occur in the real world. STAR voting also does an excellent job of balancing this utilitarian style of accuracy with a majoritarian runoff to ensure that the winner satisfies both camps. When you combine these properties with its simplicity, excellent ballot format, and highly informative pre-election polls, you end up with an amazing voting method that is absolutely worth implementing.

Ok, technically if there’s an even number of voters with a preference, then it’s possible for both candidates to be supported by exactly 50% of those voters. However, the possibility that this happens is usually just ignored since it becomes incredibly rare for sufficiently large electorates. ↩
It may have occurred to you that because of the automatic runoff, STAR would actually choose pepperoni in this scenario. While this is a downside, it ends up being a surprisingly small one. One reason for this is that if voters choose to vote strategically or even just normalize their ballots (giving the highest rating to their favorite and the lowest to their least favorite), methods like score voting that would otherwise pick mushrooms will end up picking pepperoni anyway. ↩
A new set of these simulations was recently published in the peer-reviewed journal Constitutional Political Economy. I won’t be covering them here, but I encourage interested readers to check them out. ↩
Smith//Score is a Condorcet method that sort of functions like STAR voting in reverse; it uses pairwise comparisons in its first round of tallying and scores in its second round. ↩

Why I like STAR voting: BRANDING

2022-04-01T00:00:00+00:00

I’ve discussed how STAR voting is simple, how its ballot design is superb, and how it leads to better pre-election polling. But in this post I will cover what is by far the most important aspect of this bright idea: BRANDING.

Once upon a time, there was a voting method called score-runoff voting. It was a pretty good voting method, all things considered. It produced very accurate results when tested, and its hybrid nature seemed like it might have the potential to unite the voting reform movement behind it. But there was one major problem: its name sucked.

To be fair, this is true for most voting methods. But it doesn’t have to be. Using the revolutionary technique of BRANDING, the uninspiring score-runoff voting method became the illustrious STAR voting method that you know and love. BRANDING stands for Beguiling Relatable Advertisement Notably Demands Increases in Noticed Greatness, and that’s exactly how it works. The name of the voting method itself becomes a persuasive advertisement that relates the method to the great things that voters already know about, and in doing so, it highlights those positive traits and focuses the attention on them.

Think this isn’t such a big deal? Well, just look at the names of voting methods that didn’t have the BRANDING technique applied to them. I mean, come on. First-past-the-post? More like first pass, gets roast(ed)! The Borda count? More like, the boredom mounts!¹

Compare this to STAR voting. Stars illuminate the truth for us. They remind of us of our collective potential; that if we work together, we can achieve anything, even galactic domination! Oh, and they remind us of how we all have a shot at becoming… a TikTok star or something. Hmm. Or I suppose they can be patriotic. Stars and stripes, baby!²

Ok, sorry, got a little off track there. Anyway, the name STAR voting doesn’t just create positive associations with other concepts, it also highlights the positive features inherent to STAR voting itself. Tired of electing politicians who are full of nothing but hot air? With STAR voting, they won’t be anymore (though for better or worse they may end up being full of hot plasma). Want a voting method that won’t be repealed immediately after implementation? Well, just as stars can last for billions of years, so too can STAR voting stand the test of time.

These associations can also help voters to remember how the voting method works. STAR reminds voters that the method works by having them give star ratings to the candidates. And just like the 5-pointed star, each candidate can be given a rating of up to 5 points. Stars are independent bodies³, and likewise, the ratings given to each of the candidates are completely independent of each other.

If all of this still isn’t enough to convince you of the power of BRANDING, I don’t know what will. But assuming you have been convinced, you are now finally capable of appreciating the true glory of STAR voting. Go forth, and share that glory with the world!

At least until the Borda count’s vulnerabilities to strategy lead to an excitingly disastrous election, at which point voters may find themselves longing for a return to mounting boredom. ↩
To anyone reading this who doesn’t live in the United States: my apologies for the Americentrism. ↩
Binary and multiple star systems don’t count. ↩

Why I like STAR voting: pre-election polls

2021-06-29T00:00:00+00:00

This blog post is the third in a series of posts about STAR voting. If you haven’t read the previous entries, I recommend you start with the first entry before reading this one.

Last post I explained why the 5-star ballot format used by STAR voting is superior to other commonly proposed ballot formats. In this post I’ll explain how the ballot format and voting method can be adapted for use in pre-election polls, and I’ll go over the advantages of doing so. At the time of writing no one has ever conducted a STAR voting pre-election poll, and neither the Equal Vote Coalition nor STAR Voting Action have set a standard for how this would be done. However, there is a straightforward means of transforming the STAR voting method into a pre-election poll method, and it’s this polling method that I’ll be discussing here.

A STAR voting pre-election poll, or STAR poll for short, begins by having poll respondents rate the candidates using the same 0-5 scale that STAR voting uses. Once all responses have been collected, the poll results can be calculated. These results consist of two parts. The first is the average score of each candidate. While STAR voting uses total scores to determine the finalists, it makes more sense to report average scores since they are independent of the number of respondents. This is analogous to how single-choice plurality voting elects the candidate with the greatest total number of votes, but poll and election results are commonly reported as percentages rather than totals.

While the score part of the STAR poll is straightforward, the second portion of the results is a little more involved. It consists of a pairwise preference matrix, which is simply a chart that shows how many voters prefer each candidate to every other candidate. For each pair of candidates, the example preference matrix below contains the number of voters who prefer the first candidate to the second, the number of voters who prefer the second to the first, and the number of voters who didn’t express a preference between the two.

Preference matrices in poll results will likely look a bit different from the one above. First of all, they’ll generally give percentages rather than raw totals. Secondly, they will just have one number in each box, corresponding to the percentage of voters who preferred the row candidate to the column candidate. Thus, they will look more like the example below.

	...over Allison	...over Bill	...over Carmen	...over Doug
Prefer Allison…		80%	70%	90%
Prefer Bill…	20%		40%	70%
Prefer Carmen…	30%	50%		80%
Prefer Doug…	10%	20%	10%

For this chart, the 90% in the top right indicates that 90% of voters prefer Allison to Doug. Unlike the previous chart, the number of voters who are indifferent between two candidates is not explicitly stated, but it can be found easily. For instance, the percentage of voters who are indifferent between Bill and Carmen is 100% - 50% - 40% = 10%.

While this isn’t too complicated, it can be a little overwhelming, especially when there are many candidates in the election. Because of this, I expect that poll results will often include a simplified version that only contains the candidates with the highest scores. In the extreme case, the pairwise results may only be reported for the two highest-scoring candidates, in which case a matrix is unnecessary.¹

The preference matrix and average scores together provide a lot of information about the election. The average scores serve as independent measures of how popular each candidate is relative to the others in the race.² The pairwise results can reveal the existence of a Condorcet winner, a candidate who beats every other candidate in head-to-head elections, or they can reveal that no such candidate exists. Most polls don’t come anywhere close to providing this level of information.

Consider a single-choice plurality poll. Since voters only give their top choice, it doesn’t provide an independent measurement of each candidate’s popularity. A candidate might be broadly popular with the electorate but have this support hidden since most of their supporters like another candidate slightly more. Such a poll also generally won’t provide any information about how candidates would perform in head-to-head elections against each other, since many voters won’t have either candidate in the matchup as their first choice.

Ranked choice voting³ polls can be better than this, though they aren’t always. Ranked choice polls in the United States generally have voters rank however many candidates they will be allowed to rank during the actual election. A ranked choice election is run on the poll results, and the totals for each round are reported. Below is an interactive visualization of a ranked choice poll conducted during the early 2020 Democratic Primary when there were 19 candidates in the running.

RCV Election Results by Round
Infogram

This presentation helps to simplify the results, but it does so at the cost of preventing you from seeing the totals from every round at once, which can make comparing totals across rounds annoying. Nevertheless, this is probably one of the best formats for presenting ranked choice poll results with this many candidates.⁴

One observation about these results is that because ranked choice voting only counts some rankings, many candidates have most of their support hidden. In this example, 13 candidates never made it past 5% support, and the only 4 candidates to get above 10% support already had over 10% support in the first round. Looking at the honest assessment scores from the same poll, it’s clear that candidates had much more support than the ranked choice poll revealed.

Honest Assessment Scores
Infogram

Ranked choice elections and polls are relatively new in the United States, but Australia has used ranked choice voting to elect its House of Representatives for over a century. The established polling methodology for these elections is the two-party-preferred vote. Under this polling method, all candidates except those from the two major parties are eliminated, and votes go to whichever of those candidates was ranked higher. The results of this method are essentially the same as the results of a single-choice plurality poll in which voters can only choose one of the two major party candidates, and so have all the downsides associated with plurality polls. It’s also worth noting that the two-party-preferred vote methodology only works because Australia’s House is two-party dominated.⁵

Approval polls do a better job of avoiding this trap. Under an approval poll, voters choose to approve as many candidates as they want to, and the percent of voters approving each candidate is reported. Similarly to the score portion of a STAR poll, this yields an independent measure of each candidate’s popularity. However, approval results tend to somewhat underestimate candidates’ support since voters can’t indicate that they partially support a candidate.⁶ This means that approval polls more accurately reflect candidates’ support than ranked choice polls but are still less accurate than STAR polls.

But why is it important for polls to give accurate information about how much support the candidates have? The answer has to do with strategy. Under pretty much every voting method, casting a strategic vote involves first identifying the frontrunners in the election. In the absence of good polling, voters will default to assuming that the frontrunners are the two candidates from the major parties. And this assumption itself can go on to affect later poll results. A single-choice plurality poll may show that the major party candidates are frontrunners not because they’re the most popular candidates, but because the voters being polled assumed they were the only candidates with a chance of winning and thus ignored all the others.

So the strategy under plurality voting is just to vote for whichever frontrunner you prefer, but what about other voting methods? Under ranked choice voting, the safest option is to make a frontrunner your first choice, though you can generally get away with ranking candidates that have no chance of winning above a frontrunner. How do you find out if a candidate has no hope of winning? The same way you learn which candidates are frontrunners: by looking at the polls. If ranked choice polls underestimate candidates’ support, then most voters won’t bother looking into whether they’re worth supporting. The few voters who love them will be able to safely rank them first, but that alone won’t be enough to make them viable.

Approval voting manages to do better here. The strategy under approval is to approve the frontrunner you prefer and every candidate that you like more than that frontrunner. Since approval polls do a pretty good job of accurately capturing candidates’ support, the frontrunners are likely to be the two candidates that are most popular with the electorate. But approval’s lack of expressiveness means voters may feel obligated to approve one of the major party candidates even if they truly don’t approve of either. Thus, there’s still a risk that the two major party candidates will be able to earn enough approvals to look like the true frontrunners even though another candidate is really more popular than them.

STAR voting is able to get around this problem. The strategy under STAR is to give the frontrunners different ratings so that your vote can help defeat the frontrunner you dislike most in the automatic runoff. So if under honest voting you would give both frontrunners a 0, under strategic voting you’ll want to give the one you prefer a 1. Importantly, this gives voters the option to indicate a preference between the frontrunners without fully supporting one of them. These preferences will be visible in the preference matrix, but at the same time they won’t noticeably distort the average scores, so the perceived frontrunners won’t have their popularity artificially inflated.

STAR polls combine the opportunity to avoid supporting both frontrunners (while still differentiating between them) with independent scores that serve as highly reliable measures of the support each candidate has. This means STAR polls can both collect voters’ preferences accurately and display those preferences accurately, a feat most other polling methods are unable to match. This is important because voters rely on polls to determine which candidates are worth paying attention to and how to vote strategically in the actual election. Other voting methods like single-choice plurality and ranked choice voting tend to have polls that exaggerate the support of major party candidates and underestimate the support of other candidates, leading to two-party domination.

In the final post of the series, I’ll talk about what I consider to be the most important property of a voting method: the quality of the winners it selects. For now though, I hope this post has helped you to understand what makes polls important and why STAR pre-election polls are so great compared to the alternatives (and for extra credit, you can think about how the properties that make STAR voting great for polls can carry over to the process of choosing winners in elections).

A preference matrix is also unnecessary for the top three candidates, since there are only three matchups to consider. For the top four candidates there are six matchups to consider, and past that point using a preference matrix will generally be the better option. ↩
It might sound like a contradiction to say that the scores are both independent and relative, but it isn’t. Saying that the scores are independent just means that you can adjust one candidate’s score without needing to change any of the others’ scores. The adjustments themselves are still relative to the other candidates’ scores, they just don’t affect those scores. ↩
In this post I use the term ranked choice voting to refer solely to its single-winner form, instant-runoff voting. ↩
Another option for visualizing ranked choice voting results is the Sankey diagram. ↩
A better term in this case might be two-faction dominated, as one of the factions, Coalition, is technically composed of multiple parties. However, the two main parties in the Coalition, the Liberal Party and the National Party, tend to act more like two wings of the same party than like two separate parties. ↩
The 2020 Democratic Primary poll has an example of this, though the effect may be exaggerated since the approval results represent how voters would vote under approval while the score results represent voters’ honest assessments of candidates. ↩

Why I like STAR voting: the 5-star ballot

2021-06-06T00:00:00+00:00

This blog post is the second in a series of posts about STAR voting. If you haven’t read the previous entry, I recommend you do so before starting this one.

In the previous post I made the case that STAR voting is simple enough to be a viable option for voting method reform, but I didn’t explain why STAR voting would be worth adopting. I want to start that explanation by talking about the ballot type that STAR voting uses. Often referred to as “the 5-star ballot”, it is a rated ballot with a scale of 0-5. This means that unlike with RCV ballots, you are free to rate candidates equally and to skip ratings as you like.

An example STAR ballot

The process of filling out this ballot is simple and intuitive. You start by giving your favorite candidate a rating of 5 and your least favorite candidate a rating of 0. Then you simply go down the list and rate each candidate relative to those two. An important aspect of this process is that you never have to consider all the candidates at once. If you have to, you can limit yourself to only considering at most 3 candidates at a time. This isn’t a big deal for elections with only a few candidates, but if you have an election with 20 or so candidates this could save a lot of voters from being overwhelmed.

In contrast, when filling out a ranked ballot in a 20-candidate election you’ll probably find yourself considering most or all of the candidates at once. There are ways you can avoid this, but none of them are particularly intuitive. Most likely you’ll find yourself filling in the rankings sequentially, each time considering all of the candidates that you have yet to rank.¹ Not only will this be more difficult than rating the candidates, it will also just take longer.²

Another advantage of rated ballots is that voters are less likely to spoil them by filling them out incorrectly. The single-mark ballots used for most elections in the United States have a spoilage rate of around 1-4%. Rated ballots outperform single-mark ballots on this metric with a spoilage rate of roughly 0-2%. On the other hand, ranked ballots tend to increase spoilage rates to around 4-9%.

It’s hard to say precisely why rated ballots are spoiled less often than single-mark ballots. One possibility is that voters pay more attention when they have to express a preference for each candidate, reducing the rate at which they make mistakes. However, it is quite easy to explain why ranked ballots have high spoilage rates; there are far more restrictions on how to fill them out. Voters must not give a candidate multiple rankings or skip rankings, and most of the time they are forbidden from giving multiple candidates the same ranking too.

On top of this, spoiled rated ballots can usually be partially salvaged as most candidates will have been given valid ratings. The candidates that have invalid ratings can be handled a few ways. One option is to simply count any invalid ratings as being blank, which under STAR voting means that candidate will receive a 0. Another option for when multiple ratings are given to a candidate is to default to the lowest of those ratings. But regardless of how this is handled, voters will be able to fill out rated ballots far more reliably than ranked or single-mark ballots.

A third advantage of ratings is that they do a great job of capturing information about voter preferences. Direct comparisons between ratings and rankings show that ratings have greater validity. In particular, one problem with full rankings is that they have a tendency to capture noise as they force every voter to differentiate between all alternatives. In contrast, ratings allow voters to express the differences that actually matter to them without including extra noise. Additionally, the existence of a fixed pool of candidates that all voters are rating gives voters context, allowing them to rate candidates relative to one another. This allows 5-star ballots to avoid the problems with 5-star product ratings, which arise from consumers not having the context of how good or bad competing products are or even what products are competitors.

In addition to ranked ballots, approval ballots and single-mark ballots also fall short of capturing high-quality information. Approval ballots actually do a better job at this than you might expect, but ultimately a binary evaluation of each candidate falls short of the higher resolution evaluations that the 5-star ballot enables. On the other hand, single-mark ballots are just as pathetic as you’d expect when it comes to capturing voter preferences. Asking for your favorite candidate is simply not enough.

This brings us to the final reason why 5-star ballots are great: expressiveness. Single-mark ballots, approval ballots, and ranked ballots capped at a few candidates are all much worse at allowing voters to express their preferences between the candidates. You can try to make ranked ballots more expressive by allowing voters to rank an unlimited number of candidates, but as previously mentioned this will, in practice, just lead to the collection of noise.

This leaves ballots with a greater number of ratings as the only practical option for increasing expressiveness further. However, there are diminishing returns to adding more ratings, which starts to really kick in at around 6-8 ratings. Since a 5-star ballot already has 6 ratings (remember that 0 is an option), there wouldn’t be too much of a benefit from a larger rating scale.³

A good ballot format must be easy to fill out while minimizing ballot spoilage, and it must also allow voters to express themselves while capturing voter preferences accurately. The 5-star ballot excels at balancing all of these concerns in a way that other formats simply cannot match. Single-mark ballots are more easily spoiled, barely allow voters to express themselves at all, and cannot collect enough preference information. Ranked ballots are more difficult to fill out, have very high spoilage rates, and have lower validity. Approval ballots do better, but they’re still not all that expressive and have a limited ability to collect voter preferences.

The 5-star ballot is one major reason why STAR voting is such a great method, but it’s not the only reason. Next in the series will be a post on how implementing STAR voting could change pre-election polls for the better. That post will be more speculative than this one, but I believe that pre-election polls are an underappreciated aspect of elections that deserve a closer look. Until then, just remember that single-mark ballots are terrible and we can do so much better.

Computer scientists might realize that this is a sorting problem and consider using an algorithm like merge sort that runs in O(n log n) time instead of the one I mentioned above, but even if you can perform merge sort in you head faster than you can perform selection sort, it will almost certainly still be slower than a simple O(n) rating algorithm. ↩
Many jurisdictions try to avoid these problems by limiting voters to only ranking a few candidates. This does reduce the complexity of filling out a ranked ballot some, but it comes at the cost of ballot expressiveness. ↩
My guess is that a scale with 6 ratings is a little smaller than is optimal for maximizing effective expressiveness, and the 0-5 scale was chosen primarily for marketing purposes. However, there are reasons to believe that STAR voting benefits from a smaller scale in ways that other rated methods don’t, so I don’t consider this to be an issue. ↩

Why I like STAR voting: simplicity and familiarity

2021-04-25T00:00:00+00:00

I am a big supporter of STAR voting as a practical reform for single-winner elections in the United States. Under STAR voting, voters rate each candidate on a scale from 0 to 5, the two candidates with the highest total scores become finalists, and whichever finalist is rated higher on the most ballots wins. This is where the full name—Score Then Automatic Runoff—comes from; the first round of tallying chooses the finalists based on their score totals, and then the second round of tallying is an automatic runoff with each ballot counting for the finalist that voter preferred (or counting as an abstention if the voter liked both finalists equally).

There are a lot of reasons that I like this method, but one important reason is how simple it is. As you saw above, I can describe the entire method in a single sentence. Many other competing reforms like single-winner ranked choice voting can only be partially explained in a single sentence.¹ STAR isn’t the simplest voting reform out there—that honor goes to approval voting—but I think a lot of people overestimate its complexity. Ranked choice voting, the most popular reform option in the U.S., is much more complex than STAR. If ranked choice voting can make as much progress as it has, then STAR is more than simple enough to be a viable reform, and anyone dismissing it on complexity grounds is doing it a disservice.

But STAR’s simplicity doesn’t even have to stand on its own, as it has a level of familiarity that’s rather surprising. Consider how easy it is to compare it to the familiar primary-followed-by-general election structure. The first round of STAR corresponds to a nonpartisan blanket primary, only it uses score voting rather than single-choice plurality voting. The second round then corresponds to the general election that only has the two candidates who advanced past the primary. This means that the top two runoff is the perfect jumping-off point for explaining how STAR voting improves on current voting methods. It’s easy to explain how using score for the first round prevents the vote-splitting that occurs under plurality nonpartisan primaries, and how holding an automatic runoff instead of a manual one avoids problems like inconsistent turnout and increased election costs.

Another familiar aspect of STAR is the ballot. Pretty much everyone is familiar with 5-star ratings and how to fill them out. This means that when voters encounter a STAR ballot, they’ll already understand how to use the interface. STAR voting takes advantage of this to reduce its apparent complexity even further while also reassuring voters that the ballot is collecting useful information about their preferences.²

This is all well and good as far as voter understanding is concerned, but what about actually administering elections? It turns out STAR’s simplicity extends to its implementation as well. Tabulating STAR ballots using computers is of course easy, but counting ballots by hand is also straightforward. STAR is precinct-summable, which means that tabulation only requires individual precincts to report the score totals for each candidate and the head-to-head totals for each pair of candidates, rather than reporting entire ballots as is necessary for ranked choice voting.³ STAR is also simple enough to be compatible with risk-limiting audits, so implementing it won’t compromise election security.

STAR voting isn’t the simplest method, nor is it the most familiar. If these were the only traits it had going for it, it would be an altogether unremarkable method. But we’ve only scratched the surface of what makes STAR voting a great method. In the next post I plan to elaborate more on the 5-star ballot and what makes it superior to nearly all other ballot formats. But for now, I hope you have a deeper appreciation of how simple STAR is, how it relates to concepts voters are familiar with, how easy it is to implement, and why those properties make it a viable reform.

Unless you cheat and use a run-on sentence. And I don’t mean the type of run-on sentence that’s just two sentences fused together, it has to be a really bad run-on sentence. ↩
STAR ballots actually collect better information than 5-star ratings since each voter is rating the same set of candidates instead of only rating the products/apps/whatever they happened to try out. I’ll talk more about the quality of the information that STAR collects in the next post. ↩
Alternatively, tabulation can be done in two rounds, which eliminates the need to report head-to-head totals for all pairs of candidates besides the pair of finalists (except possibly in the case of ties). ↩

Combining anarcho-primitivism and transhumanism

2021-04-01T00:00:00+00:00

Anarcho-primitivism and transhumanism are two ideologies that place a lot of importance on technology, but they do so in completely opposite ways. This makes the task of combining them into a cohesive ideology very difficult, but that hasn’t stopped people from trying. While previous attempts have had many desirable features, there is still plenty of room for improvement. As such, I wish to propose a new combination of the two which I believe makes many of the available improvements.

To build this new ideology, we first need a model of the ideologies we’re building it out of. It’s common to model anarcho-primitivism and transhumanism as being on opposite ends of a technology political axis that lies orthogonal to other axes like the left-right axis. The key to combining these ideologies will be to split this axis in two.

We’ll divide technology into two categories, which I’ll call “social technology” and “economic technology”. Social technology is technology that influences how people interact with each other. It includes things like social media, radio, and even writing. Economic technology is technology that improves people’s ability to satisfy their needs and desires. It includes things like money, agriculture, and electricity. Unfortunately, these categories aren’t all that separate. Writing is not only useful for sending letters to loved ones, it’s also useful for the record-keeping required to run an advanced economy. Likewise, money often has a big impact on how people interact with each other. The two are highly intertwined.

My proposal is for this new ideology to be a project centered around disentangling these categories. The goal of this endeavor would be to minimize the use of technology for social purposes while maximizing its use for economic purposes. The intent would be to keep the gains made in areas like healthcare and wealth while eliminating the losses in areas like social cohesion and trust.

To separate these categories, each technology will need to be classified as either economic or social, even if it fits into both categories. If the technology is classified as economic, it will remain and its improvement will be actively encouraged, but there will be a ban (informal or otherwise) on using it for social purposes. If the technology is instead classified as social, its usage will cease so as to foster a more natural social environment.

As more and more economic technologies are separated from their social consequences, at least to the degree that this is possible, society’s efforts will start shifting toward developing these technologies further and toward developing entirely new technologies that can similarly be classified as economic. The gains made from these technological improvements will enable even faster innovation, creating a positive feedback loop without the drawbacks associated with accelerated changes in social technology.

Ultimately I believe this ideology has a lot to offer for both transhumanists and anarcho-primitivists. Transhumanists get to keep enough technology to allow the construction of a pretty glorious transhumanist future. Anarcho-primitivists get to destroy the social structures that lead to oppression and alienation. This proposal likely won’t quite satisfy either group; that’s just unavoidable when combining opposite ideologies. But I think it’s a coherent ideology that’s worth exploring further.

On dealbreaker voting criteria

2021-03-07T00:00:00+00:00

In my previous post, I argued that probabilistic analysis was superior to pass/fail analysis as an approach to social choice theory. As a quick recap, pass/fail analysis tries to identify desirable criteria, then figure out which methods pass them and which methods don’t. Probabilistic analysis instead tries to identify how often failures of these criteria occur and how severe those failures are.

One consequence of pass/fail analysis is that it’s tempting to adopt what I would call a “dealbreaker criterion”, a voting criterion which a voting method must pass for you to even consider recommending it. If a voting method fails that criterion, it doesn’t matter if it is otherwise great; that failure is a dealbreaker. I’m not sure how many people actually do this, but I do know that it’s common to pick a criterion to emphasize as being crucial, which at the very least comes close.

A good example of this would be the favorite betrayal criterion, which is passed if voters are never incentivized to give less than maximum support to their favorite candidate. One of the leading voting reform organizations, the Center for Election Science, places a lot of emphasis on this criterion. In their FAQ page, the first bullet point after the question “How is approval voting better than our current system?” is “Voters can always vote for their favorite candidate, whether they have a good or bad chance of winning”. The two single-winner methods they support, approval voting and score voting, both pass the favorite betrayal criterion. At the very minimum this is quite close to being a dealbreaker criterion for them, and it’s highly likely that some of their members do hold it as a dealbreaker criterion even if the organization doesn’t quite do so.

Having a dealbreaker criterion means that you care about pass/fail analysis for that criterion, since you’re not interested in supporting any method that fails it. It doesn’t matter if a voting method fails favorite betrayal only 1% of the time; you want to feel 100% safe about voting for your favorite, not 99%! While this seems like a reasonable position to take, it leads to some surprising conclusions.

For example, while single-winner approval voting passes the favorite betrayal criterion, the proportional version that the Center for Election Science supports does not. In fact, essentially no proportional method passes this criterion, including every method currently in use, so adopting it as a dealbreaker pretty much means opposing proportional representation. This is not at all obvious, and I expect that most proponents of the favorite betrayal criterion haven’t really wrangled with this implication, especially if they consider favorite betrayal to be a dealbreaker.

This sort of thing happens often enough that it’s turned me off of having any dealbreaker criteria. As a couple more examples, the Center for Range Voting strongly supports the participation criterion, but recommends reweighted range voting even though it fails participation. Likewise, the Equal Vote Coalition strongly supports the cancellation criterion, but recommends allocated score voting even though it fails this criterion. It’s debatable whether the level of support for these criteria is high enough for them to truly be dealbreakers, but even if we assume they aren’t, it’s clear that adopting them as dealbreakers would have surprising consequences for those organizations’ recommendations.

This is another reason I dislike pass/fail analysis. The way it encourages people to adopt dealbreaker criteria can lead them to quickly reject voting methods without thinking through whether the failure of that criterion is really bad enough to dismiss the method. Under probabilistic analysis, this approach is much less natural than one that weights failures of criteria based on how frequent and severe they are, which captures a lot more information than simply having a dealbreaker criterion.

Social choice theory paradigms

2021-01-24T00:00:00+00:00

Within social choice theory, there are two major approaches to evaluating voting methods: pass/fail analysis and probabilistic analysis. Pass/fail analysis primarily consists of defining mathematical criteria that seem desirable to have, then proving which methods pass them and which methods fail them. It also has other aspects like proving that certain sets of criteria cannot all be satisfied by the same voting method; this is where the famous Arrow’s impossibility theorem comes from. On the other hand, probabilistic analysis does away with this and instead assesses voting method performance using simulations and, where possible, data from real-world elections. This approach has its downsides, but overall I think it is by far the superior evaluation method.

As a simple example of the limitations of pass/fail analysis, I’d like to consider reversal symmetry. Reversal symmetry is passed if reversing the preferences of every voter will always result in a different winner when there are at least two candidates running. The idea behind this criterion is that voting methods should not consider the best candidate to also be the worst candidate. Single-choice plurality fails reversal symmetry, since it is possible for one candidate to have both a plurality of first-choice support and a plurality of last-choice “support”, which becomes first-choice support if preferences are inverted. On the other hand, approval voting passes reversal symmetry, since the candidate with the most approvals cannot also be the candidate with the least approvals.¹

But what about a method that almost never violates reversal symmetry, but can do so in a very specific type of scenario? Enter STAR voting. For elections with fewer than 3 candidates, STAR voting will never fail reversal symmetry, and the same holds for elections with more than 3 candidates. However, there is one type of 3 candidate election that causes STAR to fail reversal symmetry.

Number of Voters	Candidate A	Candidate B	Candidate C
2	5	3	0
3	0	1	2

Here, Candidate A receives 10 points, Candidate B receives 9 points, and Candidate C receives 6 points, so A and B are the finalists. A is favored over B on 2 ballots while B is favored over A on 3 ballots, so B is the winner under STAR. What happens if we then invert these voters’ preferences?

Number of Voters	Candidate A	Candidate B	Candidate C
2	0	2	5
3	5	4	3

Now Candidate A receives 15 points, Candidate B receives 16 points, and Candidate C receives 19 points, so B and C are the finalists. B is favored over C on 3 ballots while C is favored over B on 2 ballots, so B is again the winner under STAR.

This failure only happens in elections with 3 candidates A, B, and C, where scorewise A>B>C, but pairwise C>B>A. In any other election, STAR will pass reversal symmetry. But in pass/fail analysis, STAR is just considered to fail the criterion, with no consideration as to how often this failure might occur.

This brings us to the first big problem with pass/fail analysis; it doesn’t consider how frequently a method fails a given criterion. Proving that a method passes a criterion is useful, as that tells us that the method fails it 0% of the time. Constructing an example election where a method fails a criterion is much less useful, as we have no idea whether the method fails it 1% of the time or 99% of the time. In contrast, probabilistic analysis is specifically geared toward figuring out criterion failure rates.

The other big problem with pass/fail analysis is that it ignores the severity of failures. This is especially important when it comes to strategic voting. There is a big difference between incentivizing semi-honest voting, where voters may have to rank or rate A equal to B when they really prefer A to B, and incentivizing voters to reverse their preferences, ranking or rating B above A when they prefer A to B. Likewise, there is a big difference between strategic voting leading to a slightly less popular candidate being elected, and strategic voting leading to the least popular candidate being elected. Probabilistic analysis can capture these details in a way that pass/fail analysis cannot.

As an example of this, I’d like to introduce the concept of Voter Satisfaction Efficiency (VSE). VSE is a measure of the accuracy of voting methods that is obtained using simulations. The highest possible VSE is 100%, which corresponds to always choosing the best available candidate. A VSE of 0% corresponds to choosing a candidate uniformly at random, and a negative VSE corresponds to performing worse than chance.

To calculate the Voter Satisfaction Efficiency for a given voting method, you first simulate thousands of elections under that method. You then calculate how well-liked each candidate is by the electorate, and use those values along with the knowledge of which candidate the voting method chose in each election to obtain a final value for that method’s VSE. Importantly, this cannot be done using elections in real life because we have no reliable way of determining how satisfied with each candidate each voter would be. Using simulated voters eliminates this problem, and it also allows us to use a greater number of elections for the calculation.

In addition to comparing VSE across different voting methods, we can also compare VSE across different voter behaviors. This allows us to capture details and nuances that pass/fail analysis usually misses. One great example of this is present in Jameson Quinn’s VSE simulations. In these simulations, Quinn compares a number of voting methods under several different behaviors, including all honest voters and all strategic voters. If we only focus on Borda count and score voting with a 0-10 ballot, we can see that under honesty, both have a VSE of around 97%, which is really good. However, if we switch to considering their behavior under strategic voting, we find that score now has a VSE of 96%, which is a little lower, but not much. On the other hand, Borda’s VSE drops all the way to -11%! It turns out that rather than being a mere hypothetical, it is actually possible for strategic voting to cause one of the worst possible candidates to be elected so often that the voting method underperforms selecting a candidate completely at random. This is the sort of detail that the usage of pass/fail analysis risks overlooking.

Ultimately, the issue with pass/fail analysis lies in the “fail” part. If a method passes a criterion, then we know both the frequency and severity of failures, which is very useful. It’s when a method fails a criterion that we find ourselves knowing that the method isn’t perfect, but almost nothing else.

For simplicity, we ignore all elections in which ties occur, as is common in pass/fail analysis. ↩

The motivation behind SPSV, part 5

2020-10-27T00:00:00+00:00

This blog post has been adapted from a series of posts written for r/SimDemocracy. If you haven’t read the previous entries, please start with part 1.

In the last post, we went over how RRV extends SPAV to work with 0-n rated ballots. I mentioned that SPSV also extends SPAV to work with such ballots, but that it does so using a different method. In this post, I want to start off by explaining how this method works and why I find it superior to RRV’s approach. After this, we can move on to the full explanation of the motivation behind SPSV and to comparisons with other proportional methods.

Section A: The Kotze-Pereira transformation

The extension method that SPSV uses is called the Kotze-Pereira transformation, or KP transform for short. The basic idea behind the KP transform is that it’s possible to use approval ballots as building blocks for creating a score ballot. As an example, let’s use a 0-3 rated ballot that rates candidate A 0, candidate B 1, candidate C 2, and candidate D 3. We can construct this ballot out of 3 approval ballots by having the first ballot approve B, C, and D, the second approve C and D, and the third approve only D. That way, each candidate’s score equals the number of approvals they have.

This isn’t our only option though. We could also use 1 ballot that approves B and D, and 2 ballots that approve C and D. This is a problem because not only do we want to construct score ballots from approval ballots, we also want to decompose score ballots into approval ballots. Thus, we need a means of choosing a unique set of approval ballots for each score ballot.

It turns out that there’s a pretty intuitive criterion we can use. Specifically, we can restrict ourselves to only using approval ballots that “stack” on top of each other. By that, I mean there must be some way to order the ballots such that approvals are never added to subsequent ballots, only removed. Intuitively, this means that if each ballot was a row of toy blocks, then you could stack them on top of each other, like so:

B	C	D
		✅
	✅	✅
✅	✅	✅

In contrast, the second set of ballots cannot be stacked on top of each other:

B	C	D
✅		✅
	✅	✅
	✅	✅

If the approvals were toy blocks, the approval for B would need to floating in the air. If we try to solve this by moving the B and D ballot to the bottom, we find that the approvals for C would need to be floating. Thus, there is no valid way to stack these ballots.

It turns out that there is exactly one set of approval ballots that act as stackable building blocks for every possible score ballot. Constructing this set is simple: if a candidate receives n points from a score ballot, stack n approvals in that candidate’s column. Once you’ve done this for every candidate, the rows will form the desired approval ballots.

This is how the KP transform transforms a 0-n score ballot into n approval ballots. From here, it’s simple to describe how SPSV works: run the KP transform on every voter’s score ballot, then run SPAV on the resulting approval ballots. That’s it. That’s the entire voting method.

Section B: Comparison with RRV

It’s probably not clear whether the above process gives results that differ from those that RRV gives. However, since RRV and SPSV are considered different methods, you can probably guess that the answer is yes. It may not be immediately apparent what the differences are, but after exploring a simple example they should be much clearer.

First, let’s look at how electing a bunch of candidates that a voter slightly supports affects their ballot weight. We’ll consider an election with candidates A-G, where the voter rates A 5 and all other candidates 1. C will be elected first, then D, then E, and so on. We’ll look at how many points this voter’s ballot contributes toward both A and B as more candidates are elected, under both 0-5 RRV and 0-5 SPSV.

Candidate	Method	N/A	C	D	E	F	G
A	RRV	5	4.17	3.57	3.13	2.78	2.5
A	SPSV	5	4.5	4.33	4.25	4.2	4.17
B	RRV	1	0.83	0.71	0.63	0.56	0.5
B	SPSV	1	0.5	0.33	0.25	0.2	0.17

Let’s start with candidate A. Both methods start with the original score of 5. After C is elected, we can see that RRV has deweighted the ballot more harshly, going down to a 4.17 compared to SPSV’s 4.5. By the time G is elected, RRV has deweighted the ballot all the way to 2.5, while SPSV has only now reached 4.17. If we were to continue electing candidates with a rating of 1, RRV’s rating will approach 0 while SPSV’s rating will approach 4.

Moving on to candidate B, both voting methods start with a score of 1. The election of C prompts RRV to reduce the score to 0.83, while SPSV brings it all the way down to 0.5. Once G has been elected, RRV finally reaches 0.5, while SPSV is now all the way at 0.17. Continuing to elect candidates rated 1 would lead to both scores approaching 0, but SPSV’s score does so quicker than RRV’s.

This example shows that SPSV prioritizes preserving the strength of ratings for highly-preferred candidates, and deprioritizes preserving the strength of ratings for weakly-preferred candidates. This effect is strongest when the deweighting results from electing a weakly-preferred candidate. In contrast, RRV deweights all ratings equally, regardless of how preferred the elected candidate was. Personally, I think SPSV interprets my ballot in a more faithful way than RRV does, and I would guess that most people would feel similarly.

Section C: Visualizing representation accuracy

When it comes to choosing a good voting method, how faithfully it interpets ballots is not the only important factor to consider. We also want to take into account the accuracy of the voting methods in question.

In order to visualize this, I’m first going to have to set up the scenario in which the elections take place. In this scenario there are three factions: the cyan group, the magenta group, and the yellow group. There are three seats available, and each group is running three candidates. Every voter gives the same ratings to candidates if they are from the same group. Those ratings are as follows:

Voter Group	Cyan Candidates	Magenta Candidates	Yellow Candidates
Cyan	10/10	0/10	3/10
Magenta	7/10	10/10	0/10
Yellow	0/10	5/10	10/10

At this point, the only detail we haven’t covered is the distribution of the three groups of voters. I’ve saved this for last because we actually won’t be looking at a single distribution of the three groups, but rather all of them.

This is an example of a ternary plot. This particular ternary plot shows the proportion of the electorate that each group makes up. In the top-left corner, the electorate consists of only cyan voters. In the top-right corner, the electorate consists of only magenta voters. And if you couldn’t guess, in the bottom corner the electorate consists of only yellow voters. As you move closer to the center, the mix of voters becomes more even, until you reach the center where each faction makes up exactly 1/3 of the electorate.

Now that you’ve seen the voter distribution, we’re going to look at what the winners look like for each of these possible electorates. We’ll start with a method we covered a while back, D’Hondt. Since D’Hondt uses single-mark ballots, each group will simply vote for a candidate from their faction. The distribution of winners looks like this:

Here, the colors represent how many candidates were elected from each faction. In the top-left, all elected candidates were from the cyan faction, so the area is colored cyan. Below that, we see a greenish-aqua color. This represents the election of two cyan candidates and one yellow candidate. If we then move to the right, we see a gray area that represents the election of one candidate from each group.

As you can see, D’Hondt behaves pretty nicely when voters can easily be divided into factions. However, because it uses single-mark ballots, it cannot take into account anything other than voters’ first preferences. Thus, even in this favorable scenario it still can’t behave optimally.

Next, we’ll take a look at how RRV behaves.

There are a couple things to notice here. First of all, this plot doesn’t look nearly as nice as the one for D’Hondt. This is pretty much an inevitable result of using information beyond first preferences. However, RRV actually doesn’t do that bad, all things considered. If you’re curious, you can check out how other proportional rated methods perform for yourself; you’ll see that many of them have larger concave areas and appear far more irregular than RRV does.

Moving on, the other thing to notice is that the plot is no longer symmetrical. Looking at the corners, the cyan area is larger than the other two, and the yellow area is the smallest. This reflects how the cyan candidates each receive 7 points from every magenta voter, and thus have a lot of second-choice support. Yellow, on the other hand, has very little second-choice support, and this is reflected in its smaller area.

The last method we will look at is, of course, SPSV. Here is its plot:

Overall, it looks pretty similar to RRV’s plot, which makes sense given that they are both extensions of SPAV. The main difference is that the center region is larger while the corner regions are all smaller. In fact, SPSV’s regions vary in size less than RRV’s do. The variance between the different corners hasn’t changed much, since SPSV still takes second choices into account. However, RRV had an oddly small center region, indicating that it is biased toward only representing two factions.

This is easier to observe if we increase the number of seats available. Below are the plots for RRV and SPSV when filling 10 seats instead of 3.

As you might’ve guessed, the top plot is for RRV while the one below is for SPSV. The region outlined in black on each plot is the area in which all 3 factions have at least one candidate elected. In RRV, this area is really small, around 1/4 the size of the whole ternary plot. In SPSV, this area takes up all but the outer edge of the plot. A faction will only be completely excluded by SPSV if it makes up a really small proportion of the population, in which case there simply aren’t enough seats to fairly include them.

I hope that everyone reading this feels that they have a better understanding of SPSV, or at least enjoyed themselves along the way. I know that this stuff can seem very complicated, and I’m not always able to explain things well. I encourage you to comment below with any questions you may have, and I’ll do my best to make things clearer. Thank you for reading! ❤️

The motivation behind SPSV, part 4

2020-10-26T00:00:00+00:00

This blog post has been adapted from a series of posts written for r/SimDemocracy. If you haven’t read the previous entries, please start with part 1.

In the last post, we considered how to improve upon the strange behavior that D’Hondt has when dealing with voters that have preferences which don’t match up with party lines. We went over how SPAV modifies the approach that D’Hondt used by reweighting individual ballots instead of a party’s full set of votes, and how this allows it to handle more complex voter groups in a sensible manner. This gave voters more freedom to express their preferences, but they still had to either fully support or not at all support each candidate.

Can SPAV be adapted to use 0-n rated ballots instead of approval ballots? As it turns out, this is fairly straightforward to do. Instead of using the formula 1/(1 + m), we can use 1/(1 + s/n), where s is the sum of all the scores given to candidates who have already been elected. This method is known as Reweighted Range Voting (RRV), where range voting is used as a synonym for score voting.

If n is 1, then s will simply be the number of already elected candidates who were given a score of 1, which means it will have the same value as m. Thus, RRV behaves exactly the same as SPAV when n = 1. In fact, this occurs in any instance where it is guaranteed that s/n = m, which corresponds to voters choosing to use only the minimum and maximum scores, not any intermediate scores. This parallels how score voting behaves like approval voting when voters don’t use intermediate scores.

Now that we know how RRV can behave similarly to SPAV, let’s consider how it can behave differently. Under SPAV, when a candidate a voter liked was elected, the ballot weight would change to the next number in the sequence 1, 1/2, 1/3, 1/4, etc. However, under RRV the next weight always depends on how much the voter liked the candidate. As an example, let’s consider a single 0-5 ballot in a 7 candidate election under RRV. The ballot has been cast as follows:

Candidate	Rating
A	5
B	1
C	2
D	5
E	4
F	0
G	2

Here’s a table showing how the weight of the ballot changes after the election of each candidate.

Candidate Elected	Rating	New Ballot Weight
None	N/A	1
A	5	1/2
C	2	5/12
F	0	5/12
E	4	5/16
B	1	5/17
D	5	5/22
G	2	5/24

This reveals a rather interesting pattern. If we rewrite 1 as 5/5 and 1/2 as 5/10, then the denominator always increases by the score given to the elected candidate. And looking back at our formula, if we multiply both the numerator and the denominator by n, we find that it is equivalent to n/(n + s), which in this case is 5/(5 + s). Since s is the sum of all the scores given to candidates who have already been elected, it will start at 0 and increase by the score given to the elected candidate each round, and thus we have our pattern. While this isn’t the standard way to write this formula, I find that it gives more intuition for how the weights of the ballots change as candidates are elected.

While this is a pretty nice method of extending SPAV to 0-n rated ballots, it isn’t the only way of doing so. In the next post, I’ll explain the alternate method that SPSV uses and compare it to this one.

The motivation behind SPSV, part 3

2020-10-25T00:00:00+00:00

This blog post has been adapted from a series of posts written for r/SimDemocracy. If you haven’t read the previous entries, please start with part 1.

In the previous post we went over how going from closed party-list to D’Hondt allowed voters to have a say in which candidates are elected from each party while still maintaining proportionality. However, we were still using single-mark ballots like those employed under plurality voting, also known as first-past-the-post. This meant each voter could only support one candidate along with that candidate’s party.

This causes two problems, one with allocating seats to parties and one with assigning seats a party won to that party’s candidates. First of all, because voters can only support a single party, similar parties risk splitting the vote with each other. Because seats are assigned proportionally, this isn’t too much of a problem, but when D’Hondt has to decide how to round the level of support for each party to allow an integer number of seats to be assigned, it will tend to favor larger parties at the expense of smaller ones. Tweaking the formula can change what size of parties are favored, but it cannot remove the favoritism.

The second problem is that within a party, seats are assigned using what is essentially multi-winner plurality voting. This leads to a potentially much more severe vote-splitting problem than what occurs between parties. Thus, factions within a party are incentivized to run the minimum number of candidates that they predict will be able to win seats, which will often just be 1 or 2. If a party is uniform enough to not have factions, then internal vote-splitting will likely be far less of a concern than it is for other parties.

One possible idea for solving this problem is switching to rated ballots. When D’Hondt was proposed in SimDemocracy, it used 0-5 rated ballots, not single-mark ballots. Perhaps this could solve the problem? For simplicity, instead of 0-5 ballots, I will consider switching to approval ballots instead. Since approval ballots are equivalent to 0-1 rated ballots, any insights gained should transfer over to more expressive ballots as well.

The first proposal for a form of D’Hondt with rated ballots was quite simple: all it did was replace the number of votes a candidate or party earned with the number of points that candidate or party earned. With approval ballots, this would simply be the number of approvals earned. Unfortunately, this turns out to be a very bad idea. Since parties can gain extra approvals by running more candidates, they are incentivized to run as many candidates as they can. In an extreme (albeit unrealistic) case, a party could win every single seat with only 1 voter just by running enough candidates.

It is possible to fix this problem and restore proportionality while still using approval ballots. Instead of taking the number of approvals earned for each party, we can use the number of approvals earned divided by the number of candidates the party ran. So if a party ran 1 candidate, it would get 1 point from every voter approving its candidate, and if another party ran 5 candidates, it would get 1 point from every voter approving all 5 of its candidates. Thus, running more candidates cannot automatically give a party more seats.

However, this new method still has a weird way of interpreting its ballots. For voters who support a single party but choose to vote for only some of its candidates, even though they clearly prefer this party to all others, they won’t give that party their full support. Instead, rated D’Hondt notices that they decided to only vote for some fraction of the party’s candidates, and thus has them give the party that fraction of the maximum possible amount of support.

Rated D’Hondt behaves even more weirdly when a voter doesn’t vote within party lines. As an example, consider a voter who doesn’t care about ideology much, and instead votes mostly based on which candidates they believe are the most competent. It is very likely that such a voter will approve candidates from many different parties. However, when it comes time to allocate seats, rated D’Hondt will only be able to see party divisions. It cannot allocate seats for competent candidates unless those candidates decide to leave their parties and form a new one, which is unlikely and shouldn’t be necessary.

Ultimately, what we need is a more general form of proportionality, one that accounts for the fact that rated ballots allow voters to support candidates from multiple parties and choose which of a party’s candidates to support. It actually turns out that multiple such forms of proportionality exist. However, if we want a method that behaves similarly to D’Hondt, we’ll want to look at sequential proportional approval voting.

Because of its long name, sequential proportional approval voting is usually just abbreviated as SPAV. SPAV allocates seats one at a time like D’Hondt does, but it gives them directly to candidates rather than giving them to parties and then choosing candidates. The first seat just goes to the candidate with the most approvals. For the next seat, each ballot that approved of the winning candidate is given a weight of 1/2, which means it only gives half of an approval to each candidate it approves; then the candidate with the most weighed approvals wins the second seat. This continues for each available seat, with every ballot having a weight of 1/(1 + m), where m is the number of candidates approved on that ballot that have won seats so far.

We can demonstrate both SPAV’s proportionality and its similarity to D’Hondt by looking at an example election where all voters vote exactly along party lines. Once again we can reuse our example from the first post. 50 voters will support candidates A1-A10, 30 voters will support candidates B1-B10, and 20 voters will support candidates C1-C10. We’ll assume that ties are broken in alphanumeric order (the order where A1 comes before A2, which comes before B1). The election proceeds as follows:

Round	A1-A10	B1-B10	C1-C10	Winner
1	50	30	20	A1
2	25	30	20	B1
3	25	15	20	A2
4	16.67	15	20	C1
5	16.67	15	10	A3
6	12.5	15	10	B2
7	12.5	10	10	A4
8	10	10	10	A5
9	8.33	10	10	B3
10	8.33	7.5	10	C2

If the numbers in this table look familiar, it’s because they’re the exact same numbers that appeared in the table for D’Hondt in the last post. And as you would expect, the winners included 5 candidates from party A, 3 from B, and 2 from C. However, SPAV achieved this result without knowing anything about which candidates belonged to which parties. Instead, it used the fact that there was a group of ballots approving A1-A10, another group approving B1-B10, and a third group approving C1-C10.

But importantly, this approach extends to cases where the ballots can’t be neatly divided into groups. Since every ballot is reweighted individually, SPAV can handle complex relations between partially overlapping groups that methods like D’Hondt don’t even try to deal with. This makes it a major improvement in terms of the types of preferences that voters can express.

However, there’s still room to improve upon this. Right now voters must decide between fully supporting a candidate and not supporting a candidate at all. But we know that rated ballots can allow voters to express significantly more nuanced opinions. The next post will take a look at a proportional method that’s similar to SPAV but can handle ballots with more ratings.

The motivation behind SPSV, part 2

2020-10-24T00:00:00+00:00

This blog post has been adapted from a series of posts written for r/SimDemocracy. If you haven’t read the previous entry, please do so.

We’ve seen that closed party-list gives more representative outcomes than non-proportional methods like bloc score. However, it also failed to give voters a say in which candidates from a given party would be elected. In the previous post’s example election, this didn’t matter since the voters didn’t have opinions on the individual candidates anyway. But what happens when they do have such opinions, as is the case in real elections?

If the parties all share their voters’ preferences, then this isn’t a problem since the party can just choose the candidates the voters want. But if party insiders prefer a different set of candidates, then the voters could feel cheated out of their say in which candidates get elected. Needless to say, this should not happen in a legitimate election.

One way of fixing this problem is to switch to the D’Hondt method. This method is named after Belgian mathematician Victor D’Hondt, who came up with it in 1878. However, it was actually first proposed by Thomas Jefferson in 1792, so it is sometimes referred to as Jefferson’s method instead. Instead of casting a vote for a single party, voters cast their vote for a single candidate, as is done under single-choice plurality voting. These votes are then used to determine both how many seats each party gets and which candidates from each party are elected.

To allocate seats, every party is assigned the votes received by each of its candidates. The first seat is given to the party with the most votes. For the next seat, the party that won the first seat has its total number of votes halved, and then the party with the most votes remaining wins. This continues for each available seat, with every party having 1/(1 + m) of their original vote count, where m is the number of seats that party has won so far.

This can be thought of as splitting that party’s votes between the seats they’ve already won and the seat they’re trying to win each round. If a party already has 3 seats, then it only has 1/(1 + 3) = 1/4 of its votes remaining since if it won another seat, it would have to split its votes among the 4 seats to justify having all of them. Thus, it can only afford to put 1/4 of its votes toward winning a new seat. This ensures that each seat has approximately the same number of votes allocated to it, as a party that wins 4 seats will have needed about 4 times as many votes to do so as a party that wins 1 seat.

Once all seats have been allocated, it is simple to assign candidates to them. For each party, assign the first seat that party won to the candidate from that party with the most votes, assign the second seat to the candidate with the second-most votes, and so on. This allows the voters supporting each party to have a say in what candidates from that party get elected.

In the last post, we went over an example election where the parties A, B, and C ran for 10 seats, and A was supported by 50 voters, B by 30 voters, and C by 20 voters. Closed party-list elected 5 A candidates, 3 B candidates, and 2 C candidates, thus giving a proportional outcome. Using D’Hondt will also result in this outcome, as is demonstrated by the table of vote counts below.

Round	A	B	C
1	50	30	20
2	25	30	20
3	25	15	20
4	16.67	15	20
5	16.67	15	10
6	12.5	15	10
7	12.5	10	10
8	10	10	10
9	8.33	10	10
10	8.33	7.5	10

While the party proportions are the same, the difference is that D’Hondt will ensure that the elected A candidates are the 5 A candidates with the most votes, and same for the other parties. D’Hondt also specifies how to deal with scenarios where perfect party proportionally is impossible without fractional seats.

Overall, this method gives voters strictly more choice than closed party-list did. However, it still limits voters to supporting a single candidate and a single party. In the next part, we’ll look at some proposals for altering this method to resolve this issue.

The motivation behind SPSV, part 1

2020-10-23T00:00:00+00:00

This blog post has been adapted from a series of posts written for r/SimDemocracy.

Sequential proportional score voting (SPSV) is a multi-winner voting method and a form of proportional representation. Like score voting, it uses rated ballots, and it is party-agnostic, meaning it does not take into account which parties the candidates are from. Currently, the only known instance of this method being used is the subreddit r/SimDemocracy, which uses it to elect its legislature.

Before SimDemocracy used SPSV, it used a method known as bloc score. This method was simpler to understand, but it had major issues when it came to electing a senate that represents the voters. This occurred because it was not a proportional method.

As an example of why proportionally is important, let’s consider an election with 3 parties: A, B, and C. A is supported by 50 voters, B by 30 voters, and C by 20 voters. For simplicity, we’ll say that there are 10 seats and each party runs 10 candidates. We’ll first consider this election under bloc score, and then we’ll consider it under closed party-list, a proportional method.

Under bloc score, voters rate each of the candidates, and the candidates with the highest total scores win. Since each voter supports exactly one party, we’ll assume that they give all candidates in that party the maximum rating, 5, and all other candidates the minimum rating, 0. This means that the A candidates each have 250 points, the B candidates 150 points, and the C candidates 100 points. Thus, bloc score will elect the 10 A candidates. This is clearly not representative; A has only 50% of the vote, but has total control over the elected body.

Closed party-list works very differently. Instead of rating candidates, voters cast their vote for a single party. Each party wins seats in proportion to how many votes they receive. In this case, A receives 50 votes, B receives 30 votes, and C receives 20 votes. Thus, closed party-list will elect 5 A candidates, 3 B candidates, and 2 C candidates. This results in the elected body having a makeup that closely resembles the makeup of the voters, and so is far more representative.

While closed party-list gives far more representative outcomes than a non-proportional method like bloc score, it also has a lot of disadvantages. One is that voters don’t get any say over which candidates from a party are elected; instead, that’s determined by party insiders. SPSV is much better, but it’s easiest to build up to it rather than diving straight in. Thus, the next part will cover a proportional method very similar to closed party-list that lets voters choose which candidates are elected, and from there we’ll keep making small changes until we arrive at SPSV itself.

The NPVIC, RCV-1, and Maine

2020-08-10T00:00:00+00:00

The National Popular Vote Interstate Compact (NPVIC) aims to subvert the Electoral College and elect the president of the U.S. by popular vote. It would accomplish this by having the states that signed on give their electoral votes to whichever candidate won the popular vote. However, the way it defines the popular vote assumes that all states will use single-choice plurality voting in their presidential elections. This is a problem, because Maine has switched its presidential elections to use single-winner ranked choice voting (RCV-1), also known as instant runoff voting.

The NPVIC website doesn’t address this possibility, but promoters have suggested that this problem would be resolved by the state explaining how its votes should be tallied. This is an unsatisfactory answer for a few reasons. First, there are multiple options for how the votes could be added. One option is to ignore the use of RCV-1 and simply count voters’ first preferences. Another option is to have Maine run RCV-1 until all but two candidates are eliminated, then count voters as having cast a plurality vote for whichever of those two candidates they preferred.¹ A third option is to hold a nationwide RCV-1 tally where voters from other states are considered to have cast ballots that ranked only one candidate. Each of these options has advantages that will appeal to some people and disadvantages that will drive others away.

A second reason why this isn’t a good solution is that it may not work if other states adopt other methods. This probably wouldn’t be an issue anytime soon; the most likely alternative to be adopted at the state level is approval voting, and there are options for adapting RCV-1 to work with equal rankings. However, in a scenario where other methods gain traction in the future, this could become very difficult. Trying to add RCV-1 ballots, 3-2-1 ballots, and ranked pairs ballots together while respecting how those voting methods operate would be a nightmare.

The final reason I don’t consider this solution to be enough is that it relies on the states agreeing on a method for adding the ballots together. If different states have different priorities, they may not be able to agree on a method. For instance, Maine may want to stay as true to its chosen voting method as possible, while other states may want a simple method that gives all voters the same options. Even if the states are cooperative with each other and try to find a compromise, the process could still take a lot of time. If it isn’t finished by the time the next presidential election is held, the election results could be severely delayed.

I don’t know what the future holds for the NPVIC. Maybe it will be unable to get enough states to pass it and simply die off. Maybe Maine will repeal RCV-1 and join the other states in sticking with single-choice plurality. Or maybe this problem will need to be dealt with at some point. If that becomes the case, things could become rather unpleasant.

Voters who didn’t rank either of the two finalists would be considered to have abstained. ↩

Quadratic voting and types of one person, one vote

2020-08-09T00:00:00+00:00

In a previous post, I laid out a hierarchy of three different possible meanings of one person, one vote (OPOV). The 1st level of OPOV required that each voter have exactly one ballot. The 2nd level required that each ballot have the same weight. Finally, the 3rd level required each possible ballot to be perfectly cancelled out by another possible ballot. I also created a combination Euler/pyramid diagram to demonstrate the relationship visually:

Before moving on, I’d like to formalize these types of OPOV a little more. I do think the 3rd level was defined well enough, but you can visit this page for the cancellation criterion if you need a refresher. For the 2nd level, it might not always be clear when the “weights” of two ballots are equal. It turns out that this has already been formalized through the anonymity criterion, which requires that for every fixed set of votes, the winner of the election remains the same regardless of which voters cast which of the votes from that set. This captures straightforward failure cases like the Electoral College, but also some stranger edge cases that might not have clear “weights” to compare.

When considering the 1st level, we run into the issue of defining what counts as “one ballot”. For a rated method with a 0-5 scale, we could give a voter an unfair advantage by giving them two 0-5 ballots and adding them together. We could also give them an advantage by giving them a single 0-10 ballot. But mathematically, these two advantages are one and the same, even though supposedly one has two ballots and the other only one.

We can solve this by requiring ballots to provide the same set of options for casting a vote to each voter. Now the single 0-10 ballot still violates this, even if it wouldn’t under a more literal interpretation of “one ballot”. I decided to formalize this idea into the identical input options (IIO) criterion. As a quick reality check, the IIO criterion is implied by the anonymity criterion, which means that any voting system¹ passing anonymity must also pass IIO. This matches up with the idea that any voting system with equally-weighted ballots should also have exactly one ballot per voter, as shown in the above diagram.

Now that we’ve formalized the types of OPOV more, we can move on to the other portion of this post’s topic: quadratic voting. Under quadratic voting, voters “buy” multiple points in favor of a single option using “voice credits”, and the option with the most points in favor wins. The cost of buying points for a given option is the square of the number of points being bought. This means that 1 point would cost 1 credit, 2 points would cost 4 credits, 3 points would cost 9 credits, and so on. Thus, the cost function ends up being quadratic.

In the previous OPOV post, I said that quadratic voting failed every type of OPOV. This is true for the version I just described, but it turns out that there are variations of quadratic voting that can pass different types of OPOV. This makes quadratic voting a useful tool for explaining how voting systems can be altered to pass or fail the various types of OPOV. In particular, I want to consider the scenario of quadratic voting being used in U.S. presidential elections.

Let’s start off by considering the case where all states switch to using quadratic voting, but still operate within the Electoral College system. We’ll assume that the voice credits persist over multiple elections, possibly (but not necessarily) because they are real currency. This means that different voters will have different amounts of voice credits in each election, and so some voters will be able to cast votes that others won’t. For example, a voter with 10 voice credits could give Candidate A 3 points and Candidate B 1 point since 3² + 1² = 9 + 1 = 10. In contrast, a voter with only 9 voice credits would be unable to cast this vote. Thus, this system fails the IIO criterion.

What happens when we modify the system to distribute a fixed number of voice credits to each voter in each election, without the ability to save them for future elections? Well, we’ve eliminated the issue of different voters being able to cast different votes, so the IIO criterion is now passed.² However, because the Electoral College is still in place, it remains possible to change the outcome of many elections by changing which voters cast which votes in each election. Thus, the anonymity criterion is still failed.

Modifying this system to pass the anonymity criterion is straightforward; all we need to do is replace the Electoral College with a national popular vote. Now every voter is treated the same regardless of what state they vote in, so there is no way to change the outcome of the election by swapping votes around. However, it’s not always possible for one voter to perfectly cancel out the vote of another voter. For example, if each voter is given 100 voice credits per election and there are three candidates A, B, and C, then one voter can cast a vote that gives 10 points to A. Perfectly cancelling this vote out would require giving 10 points to B and 10 points to C, but doing that would cost 200 voice credits, so any voter with only 100 voice credits couldn’t cast a cancelling vote. Thus, the cancellation criterion is still failed.

At this point it might feel like we’ve modified quadratic voting to pass all the types of OPOV it possibly can. However, there is a way to modify it further so that it passes the cancellation criterion; instead of restricting voters to buying points in favor of an option, we also let them buy points in opposition to an option. This means that in the example above, the vote that gives 10 points in favor of A can now be cancelled by a vote that gives 10 points in opposition to A. In fact, it will always possible to construct a valid vote that cancels out another valid vote, as we can simply reverse whether the points purchased are in favor of or in opposition to each option. Thus, this version of quadratic voting passes the cancellation criterion.

I’m hoping this demonstration of modifying a voting system to pass each type of OPOV in sequence helps build intuition for how the types relate to one another and to the voting systems that pass and fail them. If some of the vaguer types seemed arbitrary, I also hope that my efforts to provide more formal criteria helped clarify things.

In both this post and the previous post on OPOV, I kind of conflate voting methods with electoral systems under the term “voting systems”. If this doesn’t bother you, you can just ignore it. If this does bother you, you can think about this matter purely in terms of electoral systems by applying a simple default electoral system as a “wrapper” around any voting methods that are mentioned. ↩
This assumes that for each state, all candidates either make it onto the ballot or can be written in. If this doesn’t happen, then IIO is still violated. ↩

Soul harvester

2020-07-14T00:00:00+00:00

Epistemic status: fiction

Most people believe that the soul is the essence of a person. These people are wrong. The essence of a person is their consciousness, and consciousness is merely a complex and intricate set of computations occurring in the brain. The reason so many believe this myth regarding souls arises from the consequences of removing one.

The exact results vary from procedure to procedure, but what they all have in common is the destruction of the patient’s consciousness. In some cases the patient simply dies. In others they enter a permanent coma-like state. And for some procedures, the results are… best left unsaid.

The issue that all of these procedures encounter is related to the soul’s dependence on a person’s consciousness. Without a consciousness to shape it, a soul would merely be a small and unremarkable reservoir of magical energy. However, magical energy shaped directly by consciousness becomes incredibly useful.

The reason souls are so valuable is that they can be used as oracle machines, which can perform feats that should be computationally impossible. Many of the most powerful spells and rituals are dependent on the ability to solve impossible computations, and thus require the use of a soul in order to be completed.

One such spell is the Explorable Prophecy. This spell operates by simulating the counterfactual universe in which it has no effect, and then allowing the caster to explore this simulation as they please. Needless to say, this requires an incredible amount of computational power, assuming it is even computable at all. Without the existence of souls, casting a spell like this one would be entirely infeasible. With souls, this task becomes possible, albeit incredibly difficult.

Unfortunately, the utility of souls comes at a cost. The consciousness that shapes the soul does so in order to make use of its computational abilities. This was driven by evolution, but evolution is not intelligent, and so the brain does not use the soul anywhere near as effectively as it could. In fact, it does not even use it for anything it can’t do itself. But it does use the soul enough to become dependent on it. And so, if the soul is removed, the consciousness ceases to exist.

Except there was a case where this didn’t happen. I cannot divulge the specifics, but I can say that it inspired me to develop a new technique for removing souls. The key to this technique is to slowly disrupt the brain’s connection with the soul over a long period of time. The brain has enough plasticity to learn that it can no longer depend on the soul and eventually will fully take over. At this point, the soul can be removed without causing any harm to the patient.

Going into further detail about the procedure would unfortunately require me to reveal proprietary information. However, I believe what I have divulged should be a satisfactory explanation of how my product can be ethically sourced.

Why 1 is not prime

2020-07-05T00:00:00+00:00

Modern mathematicians have come to the consensus that the number 1 is not a prime number. However, many people still believe that 1 is in fact prime. This belief is justified by definitions like

a prime number is a positive whole number that is only divisible by 1 and itself

and indeed, under this definition 1 would be prime. However, most definitions are worded to exclude 1, usually by specifying that a prime number must be greater than 1.¹

But why make the definition more complicated just to prevent 1 from being a prime number? Wouldn’t it make more sense to just say it is prime? Well, it turns out that treating 1 as a prime number is quite awkward as it lacks many properties that all prime numbers have. This post will go over four of those properties, and in doing so will hopefully make the exclusion of 1 less of a mystery.

The first property is that prime numbers can only appear in an integer’s factorization finitely many times. For example, 64 can be written as 2⁶, but it cannot be written as 2⁷, 2⁸, or any other larger power of 2. This property is key to the Fundamental Theorem of Arithmetic, which states that every positive integer can be uniquely represented as a product of primes.² Thus, if you know an integer is equal to some product of primes, you also know that no other product of primes will be equal to that integer.

If we try to include 1 as a prime number, however, we run into a problem. Since 1 times any number equals that number, 1 can appear in a factorization an arbitrary number of times. As an example, 2 = 2 × 1 = 2 × 1 × 1 = 2 × 1 × 1 × 1 and so on. This means that counting 1 as a prime number breaks the Fundamental Theorem of Arithmetic, and in order to get it back we have to explicitly exclude 1 from the list of prime factors that the theorem applies to.

The Fundamental Theorem of Arithmetic is probably the most-often cited reason for why 1 isn’t prime, but on its own it may not seem to be a sufficient justification. However, there are other properties that primes have and 1 lacks. For instance, the multiples of a prime that are greater than the prime itself are all composite numbers. This fact is exploited by an algorithm for finding primes up to some limit known as the sieve of Eratosthenes. It works by finding the first prime it has yet to find, then marking all multiples of it as composite. It can then skip over those numbers when finding the next prime.

If we start the sieve of Eratosthenes at 2, everything works fine. In contrast, if we start it at 1, it immediately marks all other numbers as composite and declares 1 to be the only prime. Since all primes (and all other positive integers) are multiples of 1, the strategy employed by the sieve of Eratosthenes cannot work. Instead, it would need to be modified to skip the step of marking multiples as composite for 1. Again, we find ourselves needing to make special accommodations for 1 if we consider it to be prime.

Another instance in which including 1 as a prime creates a problem is Euler’s totient function. This function takes in a positive integer n and outputs the number of totatives n has, where a totative of n is a positive integer k ≤ n where the greatest common divisor of k and n is 1. That may feel like a lot to take in, so let’s go through an example. Consider φ(6), where φ is Euler’s totient function. To find the value of this expression, we need to find all the totatives of 6. Starting with 1, we find that gcd(1, 6) = 1, so 1 is a totative of 6. In the case of 2, gcd(2, 6) = 2, so 2 is not a totative of 6. As for the rest, gcd(3, 6) = 3, gcd(4, 6) = 2, gcd(5, 6) = 1, and gcd(6, 6) = 6. Thus, 5 is the only other totative of 6, and φ(6) = 2.

As you may have guessed, prime numbers have a unique property that involves Euler’s totient function. Specifically, for any prime number p, φ(p) = p - 1. This arises from the fact that p only has two factors, 1 and p. This means that gcd(k, p) equals p when k is a multiple of p and 1 otherwise. For k ≤ p, the only k that’s a multiple of p is p itself. Thus, every other k will be a totative of p.

When calculating φ(1), there is only a single value of k to consider, namely 1. It so happens that gcd(1, 1) = 1, so 1 is a totative of 1 and φ(1) = 1. Once again, this does not fit the pattern that the prime numbers follow. Thus, if we include 1 as a prime, we must amend our statement to say that for any prime number p except 1, φ(p) = p - 1.

Along with Euler’s totient function, the sum-of-divisors function also highlights a property of primes that 1 lacks. The sum-of-divisors function, referred to as σ, takes a positive integer as input and outputs the sum of all its positive divisors. For instance, 12 has 1, 2, 3, 4, 6, and 12 as divisors, so σ(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28. As we’ve said before, a prime number p has only two divisors, 1 and p, so it’s easy to see that σ(p) = p + 1 for any prime number. As has become quite predictable by now, 1 fails to follow this pattern. It only has a single divisor, 1, so σ(1) = 1 rather than 2 as it would if it followed the pattern.³

I hope I have succeeded in giving a more satisfying explanation of why 1 isn’t prime than whichever one (ha!)⁴ you knew of before. This was one of those aspects of math that seemed weirdly arbitrary to me when I was younger, and I am quite thankful to have a better understanding of why prime numbers are defined the way they are. The reasons for this go far beyond what I have discussed here, but I think the examples I chose do a decent job of balancing insight with simplicity.

Some definitions instead say that prime numbers have exactly two positive integer factors, which I find to be a much more natural means of excluding 1 from the primes. Nonetheless, requiring primes to be greater than 1 seems to be more common; Wikipedia, Wolfram|Alpha, and Wolfram MathWorld all use this option. ↩
This assumes that the use of the empty product is allowed. ↩
This failure can be actually be generalized to a whole set of divisor functions. Let d₁ through d_k represent the k divisors of n. Define σ_x(n) = d₁^x + d₂^x + ⋯ + d_k^x. Then for any prime number p, σ_x(p) = p^x + 1. In contrast, σ_x(1) = 1. ↩
I’m sorry. ↩

Thanos is a straw centrist

2020-04-01T00:00:00+00:00

A straw centrist is a person who always takes the middle position on issues. For example, if you asked them if we should kill all the men or not, they would say that we should kill half of the men. If you asked them if we should kill all the women or not, they would say that we should kill half of the women. And if you asked them if we should kill all the children or not, they would say that we should kill half of the children.

But it wouldn’t just be disjoint groups for which this is true. If you asked them if we should kill all the teachers or not, they would say that we should kill half of them. But how could they make sure that they don’t accidentally kill over half of the teachers while killing half of the women? Well, by the law of large numbers, there is a really simple method to ensure that they kill half of every group: choose a random sample to kill. If the sample size is equal to the size of half of the population, then they will achieve all of their goals at the same time.

Now we see how Thanos qualifies as a straw centrist: his plan is exactly what we’d expect from one. This also explains why he talks about balance all the time. A straw centrist picks the middle position on every issue because they want to balance the advantages and disadvantages of each side. In the same way, Thanos kills half the population because he wants to balance the advantages and disadvantages of killing everyone and killing no one. Therefore, it’s safe to conclude that Thanos is indeed a straw centrist.

The meaning of one person, one vote

2020-02-16T00:00:00+00:00

The concept of one person, one vote is often brought up in discussions of voting methods and electoral systems. In the United States, it’s commonly associated with a Supreme Court decision that required states to use districts with approximately equal populations. However, the general idea that everyone’s vote should be equal has been brought up as a way to challenge alternative voting methods like approval voting and instant-runoff voting (abbreviated IRV, and also called ranked-choice voting), despite the fact that votes cast under these methods are not any less equal than the single-choice plurality method used in most U.S. elections. To make this even more complicated, this concept has also been used to argue in favor of replacing plurality voting with alternative methods. The Equal Vote Coalition’s equality criterion is a good example of this.

Having all these overlapping concepts associated with one phrase is likely to lead to a lot of confusion. For instance, Equal Vote appears to equivocate between two different meanings in their page comparing STAR and IRV. The section on equality begins with the following sentence:

The U.S. Supreme Court has found unequivocally that ‘One Person, One Vote’ requires that “each vote be given as much weight as any other vote.”

However, the page goes on to claim that IRV fails one person, one vote, which is not true under the Supreme Court’s definition. Instead, Equal Vote has switched to applying their own equality criterion. Without proper clarification, this is very misleading to readers.

To help counter the confusion that can arise in this and similar situations, I’d like to construct a hierarchy of the various interpretations of one person, one vote. This hierarchy will have 3 levels, with each successive level being more restrictive than the last. Thus, passing the 2nd level means the 1st level is also passed, and meeting the 3rd level ensures that both other levels are satisfied.

The 1st level is the most literal interpretation of one person, one vote. It simply requires that every participant gets exactly one ballot. This is the version that some attempt to employ against methods like approval and IRV; their mistake is that they conceive of a vote as being a mark on a ballot rather than the ballot itself. When the latter conception of a vote is used, it becomes clear that pretty much any serious voting system passes this level of one person, one vote. However, an interesting exception to this is quadratic voting, which allows voters to “buy” multiple votes on a single issue using “voice credits”.¹

The 2nd level of one person, one vote requires that every voter’s ballot be weighted equally. This is the interpretation used by the U.S. Supreme Court to eliminate unequally-sized districts at the state level, including a pair of districts where 41 times as many voters lived in one district as did in the other. Pretty much all voting systems satisfy this requirement, assuming they use districts of roughly equal size. Alternatively, the number of representatives for a district can be kept proportional to the number of voters in that district. Note that the Electoral College fails to do this, so it does not satisfy this level of one person, one vote.²

The 3rd and strictest level of one person, one vote is the previously mentioned equality criterion, also referred to as Frohnmayer balance. The Equal Vote Coalition describes this criterion as follows:

A voting method passes the Equality Criterion if every possible vote expression has a counter-balancing vote expression and if the counting system produces the same election outcome when any pairing of a vote expression and its counter-balancing vote expression are added to the tally.

In other words, when one person casts a vote, it must always be possible for another person to cast a vote that will perfectly cancel it out, regardless of how all other votes are cast. This is actually far more restrictive than the previous levels of one person, one vote. For instance, single-choice plurality voting fails this criterion, as does the popular reform option instant-runoff voting. It’s also impossible for any multi-winner voting method that achieves proportional representation to pass this criterion.³

Some of the few voting methods that do meet this criterion are approval voting, score voting, and STAR voting. To cancel out a vote when using approval voting, you simply approve all the candidates that weren’t approved on the other ballot. This results in each candidate receiving exactly one approval from the two ballots, keeping the differences between their totals the same. Under score and STAR, you have to give the candidates the ratings opposite of those on the other ballot. For example, using a scale from 0-5, a rating of 5 would be canceled with a rating of 0, a rating of 4 would be canceled with a rating of 1, etc. This ensures that the two ballots give each candidate exactly 5 points total. In the case of STAR, it also preserves pairwise results, so the winner of the automatic runoff will remain the same as well.

To summarize, the 1st level of one person, one vote requires that each voter have exactly one ballot. The 2nd level requires that each ballot have the same weight. The 3rd level requires that each possible ballot can be perfectly cancelled out by another possible ballot. To illustrate this relationship, I’ve created a helpful combination Euler/pyramid diagram:

It’s called “quadratic voting” because the number of credits needed to buy votes for a given issue is the square of the number of votes being bought (so 1 vote costs 1 credit, 2 votes cost 4 credits, 3 votes cost 9 credits, and so on). ↩
The U.S. Supreme Court’s interpretation of one person, one vote only applies to the states, so there’s no constitutional issue here. In fact, the Electoral College system doesn’t even require states to hold elections to decide how to choose their electors. ↩
There is a proposal for a similarly strict version of one person, one vote that can be passed by proportional methods called Vote Unitarity. ↩

On normative ethical theories

2019-04-01T00:00:00+00:00

Inspired by this tweet.

There are a lot of proposals for what makes an action morally good or bad. These normative ethical theories can take various forms, but the most plausible are types of utilitarianism. This is because utilitarianism allows agents that follow it to behave rationally.

The von Neumann-Morgenstern utility theorem shows that any agent that does not behave as if it has a utility function can have arbitrary amounts of resources pumped from it. This is a huge problem for any normative ethical theory that does not allow agents to behave this way. “Moral” agents would be unable to reliably perform obviously good acts like life-saving surgery because another agent could come along at any time and trick them into giving up the surgery equipment or other necessary resources. Since this is intuitively not how morality works, morality must be some form of utilitarianism.

Does this mean that other theories are doomed? Not necessarily. It turns out that a lot of them can be easily converted into utilitarianism. For example, virtue ethics can be converted simply by holding “being as utilitarian as possible” as the only virtue worth having. Deontology can be similarly converted by making “act as a utilitarian would” the only rule.

Other theories are much harder to convert. Contractarianism requires that everyone agree to a specific social contract, so if this contract is not already equivalent to some form of utilitarianism, then it would have to be “renegotiated”. This would be a daunting task, as it would require every single member of society to consent to a new utilitarian contract. Luckily, making a few reasonable assumptions allows us to show that we must have a social welfare function that consists of a weighted sum of individual utility functions. Since this is itself a utility function, this ensures that the social contract is indeed utilitarian.

These are not the only normative ethical theories in existence. There are plenty of others which should be examined for possible equivalences to utilitarianism and discarded if they are not found to have any. Of course, it’s also acceptable to simply apply utilitarianism directly rather than through some other theory, but having different ways to frame the matter is useful for making things as intuitive as possible. This might ultimately reach a point where all normative ethical theories are either unified in this way or dismissed as irrelevant, but until then, we must make do with the equivalences we have.

The world's problems

2018-12-31T00:00:00+00:00

There are a lot of problems out there. Some of these problems are small, like whether you should get a new phone or not. Other problems are big, like how to solve climate change. But of these problems, which ones are the most important? I don’t know, of course, but I’m going to hazard a guess at them anyway.

First, a quick overview of the criteria I’m using to determine importance.¹ I’ll be considering the impact, tractability, and neglectedness of problems. Impact is simply how good solving the problem would be. Tractability is how easy it is to make progress on the problem; if all else is equal, directing the same amount of resources to a more tractable problem will result in more good being done. Neglectedness is how few people and resources are being directed at the problem. Due to the law of diminishing returns, a more neglected problem will generally be easier to make progress on than a less neglected one.²

My current guess for the 5th most important problem is poverty, which I believe can be most effectively solved through unconditional cash transfers. In developing countries, this would involve performing the work of charities like GiveDirectly. For developed countries, the goal would be the implementation of policies like universal basic income, which provides regular cash transfers to every citizen.

I’d expect solving this well to have a large positive impact by reducing human suffering and giving many people an opportunity to contribute to society that they would have otherwise been denied. The simplicity of unconditional cash transfers would make the problem very tractable. As for neglectedness, few charities are working on this, and no country has yet to implement a full UBI. If you’re interested in further reading on why these options might be worth supporting, I’d suggest starting with GiveWell’s page on cash transfers and Scott Santens’ basic income FAQ.

Improving information aggregation occupies the 4th spot on my list of problems. Thanks to the internet, access to information is no longer a problem for most people. However, it often remains difficult to determine the accuracy of a given piece of information, or to properly combine small bits of evidence to reach a solid conclusion. One technology that could help with this in many circumstances is prediction markets. Prediction markets operate via “stocks” that pay out a certain amount only if a certain event happens. Thus, the price of one of these financial instruments as a percentage of the payout amount is the probability of the event happening, according to the market. For example, if an instrument pays out $100 if Trump is reelected in 2020 and it’s trading for $38, then the market currently believes there’s a 38% chance of Trump’s reelection.

The impact of improving information aggregation would be huge, as the decision-making processes of organizations from corporations to governments would receive a substantial boost. The main issue is that popularizing prediction markets seems like a rather intractable problem, especially given that online prediction markets are effectively outlawed in the United States. On the other hand, very few people are working on this issue, and it may be the most neglected problem on this list. For additional reading on how prediction markets could be directly incorporated into a governance structure, see Robin Hanson’s futarchy.

The 3rd position goes to the problem of aggregating values. The largest improvement here was the invention of democracy, but there’s still much room to do better. The most common voting method, single-choice plurality voting, is generally agreed to be one of the worst voting methods in existence. It’s highly inexpressive, and it falls prey to vote-splitting and spoilers, which makes it hard for new candidates to run, increases polarization, and forces strategic voters to vote dishonestly.

The impact of improving value aggregation through a better voting method is quite large, as can be seen in the available improvements in voter satisfaction efficiency under alternative methods. Current voting reform efforts suggest that this is a fairly tractable problem as well. And while it’s not the least neglected problem, there seem to be few people pushing the best reforms available. For further reading, I’d start with this introduction to voting theory, which is how I was first introduced to the subject.³

The 2nd entry on the list is home to the problem of identifying important problems. It turns out that doing this is really hard, and a lot of groups have put a whole lot more effort into this than I have. Unfortunately, these groups tend to end up generating very different lists, likely in part because they use different criteria. Given that it is pretty hard to make progress on important problems if you don’t know what the important problems are, this seems like a pressing issue.

Identifying important problems would likely have a very large impact through shifting efforts from less important problems to more important ones. It appears to be somewhat tractable given the existing progress that has been made. Since people generally pick a cause to focus on without checking how well it meets these criteria, this should be a rather neglected problem as well. The effective altruism movement is an excellent place to start looking into this topic.

The only problem I find more important than identifying important problems is that of existential risks. While it is difficult to make progress on important problems if you don’t know what they are, it is impossible to make progress on them if humanity is extinct or otherwise incapable of realizing a better future. Given the astronomical amount of potential good that could be realized in the future, this would be an unacceptable loss.

I consider preserving the possibility of a good future to be one of the highest impact actions there is. Unfortunately, it’s likely one of the less tractable problems on this list, as reliably affecting the far future seems to be a difficult task. Existential risk is a very neglected problem, however, so there should still be ways to improve the situation. If you’re interested, the Future of Life Institute and the Future of Humanity Institute have some great resources on this topic.

One aspect of these problems that I find quite fascinating is how solving one can help with solving others. Someone lifted out of poverty by cash transfers may go on to discover the importance of a problem that would have otherwise gone unnoticed. Prediction markets could help identify which voting methods outperform others in specific circumstances. And preventing existential catastrophes ensures that we retain the opportunity to fix all of these other problems.

These kinds of relationships should not be too surprising; it makes perfect sense that more important problems would have many indirect effects on other problems. Of course, just because these are important problems does not mean they are the most important problems, and I expect to change my mind on some of these in the future. In particular, I feel fairly uncertain about whether eliminating poverty and aggregating information should be on this list. I’m thinking I might write a post at the end of every year giving my updated positions on this topic.

These criteria come from the effective altruism movement, though I won’t be applying them as rigorously here as others might elsewhere. ↩
A more neglected problem will also generally have less people advocating for it, which in turn means you’re less likely to have heard of it. If my choice of problems seems weird to you, there’s a good chance that this is the reason. ↩
Technically my first introduction was probably CGP Grey’s Politics in the Animal Kingdom series, but “single-choice voting is bad” is about all I took away from it at the time. ↩

Ranked choice voting is worth supporting

2018-11-26T00:00:00+00:00

Ranked choice voting (RCV) has a lot of supporters in the U.S. voting reform movement. However, the single-winner version, which also goes by the name instant-runoff voting (IRV), does have some detractors, particularly among those who support rated voting methods instead. Most still agree that RCV is an improvement over the single-choice voting method¹ used in almost every U.S. election, but a few dispute even this. While I believe that RCV is likely not the best single-winner method, I also believe that it is an improvement over single-choice voting. As such, I think you should support RCV even if you agree with many of the arguments made against it.

The first argument I will address is RCV’s failure of the favorite betrayal criterion. The favorite betrayal criterion requires that a voting method never allows a voter to get a worse result by giving their favorite candidate maximum support. RCV’s failure of this criterion means there are situations in which a strategic voter will “betray” their favorite candidate by ranking them lower than another candidate. In other words, a voter’s favorite candidate may sometimes act as a spoiler that must be ranked lower than a more viable candidate in order to avoid the voter’s least-preferred outcome.

But wait, doesn’t RCV eliminate the spoiler effect? Well, it depends on what you count as a spoiler. If you’re only concerned with scenarios where a minor candidate with only a few percent of the vote changes which of two major candidates wins, then yes, RCV eliminates spoilers. But if you also want to take into account scenarios where this candidate builds up enough support to beat the most similar major candidate, only to lose to the other major candidate, then RCV fails to eliminate all spoilers.

However, it’s important to keep in mind that single-choice voting doesn’t eliminate any of these spoilers. So if you’re deciding between it and RCV, it’s hard to argue that RCV is worse because it fails the favorite betrayal criterion and allows spoilers. After all, single-choice voting also fails the favorite betrayal criterion and allows even more spoilers! Therefore, while this may be relevant when comparing RCV with other voting methods, it cannot serve as a reason why RCV is worse than single-choice voting.

Another argument made against RCV is that it is non-monotonic. This means that there exist RCV elections in which it is possible for a winner to become a loser by receiving more support or vice versa. For example, consider these two scenarios involving candidates A, B, and C:

Number of Voters	Rankings	Number of Voters	Rankings
5	A > B > C	5	A > B > C
6	B > C > A	8	B > C > A
6	C > A > B	4	C > A > B

In the first election, A is eliminated in the first round, and B goes on to win 11 to 6. In the second election, two of the voters who ranked B last in the first election have switched to ranking B first, increasing support for B. However, when the results are found, C is eliminated in the first round, and then A wins 9 to 8!

This behavior is a problem because it seems impossible to justify both outcomes. If it is correct for B to win the first election, then if support increases for B but not the other candidates, surely it must be correct for B to win the second election. Likewise, if it is correct for B to lose the second election, then if support decreases for B but not the other candidates, it intuitively must be correct for B to lose the first election. Thus, for every non-monotonic pair of elections, at least one outcome is incorrect. This implies that at least 50% of non-monotonic elections² choose the wrong candidate.

However, to know how much of an effect non-monotonicity has, we also need to know the frequency of non-monotonic elections. Estimates for this show anywhere between 5% and 16% of elections to be non-monotonic. Even worse, when elections where RCV gives the same result as single-choice voting are excluded, estimates jump to between 9% and 36% of elections being non-monotonic. Compare this to single-choice voting, which is a monotonic method and therefore has a 0% rate of non-monotonicity. It seems like non-monotonicity succeeds as an argument against replacing single-choice voting with RCV.

But this argument ignores bad election results that arise for reasons other than non-monotonicity. If you really want to assess the accuracy of a voting method, you’ll need to be much more thorough. Luckily, there’s a way to do this called Voter Satisfaction Efficiency (VSE). VSE is calculated by running tons of simulated elections and determining how satisfied voters are as a group with each result. A VSE score of 100% means the voting method always picks the candidate that maximizes voter satisfaction, and a VSE score of 0% means the voting method maximizes voter satisfaction as poorly as randomly selecting a candidate would.

RCV earns VSE scores between 79% and 92%, depending on how strategic voters are. However, single-choice voting only earns between 71% and 86%. This means that despite being monotonic, single-choice voting fails to match RCV’s performance when it comes to voter satisfaction. RCV is simply a more accurate method.

Perhaps the most concerning argument against RCV is that it risks “poisoning the well” for voting reform. Even though it performs better than single-choice voting, problems like non-monotonicity giving unintuitive results may lead to RCV being repealed. When a method that doesn’t have these problems is proposed by a different group of reformers, voters will choose to vote it down since they have no reason to believe this group of reformers has a better proposal than the last one did.

This isn’t entirely hypothetical. There have been several instances where RCV has been repealed, and it intuitively seems like it would be bad strategy to try pushing another voting method in any of those cities. However, an important component of why this seems like a bad strategy is that there would be many other places to try this instead. This suggests that the actual damage that RCV would cause to the movement would be minimal, since you can always just go somewhere RCV hasn’t been tried.

On the other hand, there is a very real risk that opposing a method as popular among reformers as RCV is could tear apart the voting reform movement. In my opinion, the worst-case scenario for the movement is that it splits into pro-RCV and anti-RCV factions that each actively oppose the method(s) preferred by their counterpart. In this “nightmare scenario”, the factions’ fights with each other make it easy for those who benefit from single-choice voting to keep it in place, since they can always get help from one faction to fight the other.

This may strike many as an outlandish scenario, and I hope that it is in fact that improbable. But at the very least, I fear that some less extreme scenario could actually occur and make reform that much more difficult. And we desperately need reform right now. So for the sake of ending single-choice voting, I ask that you support RCV, even if, like me, you don’t think it’s the best option out there.

There’s one final point I’d like to make. Most campaigns for voting reform are currently occurring at the local level, and those that aren’t are still only at the state level. There’s currently plenty of room for multiple methods to coexist. Supporting RCV does not meaningfully decrease the opportunities available to promote your favorite method. As long as this remains the case, maintaining unity is more important than implementing the absolute best method on every occasion.

If you weren’t willing to support RCV before, I hope I’ve convinced you to start doing so, if only grudgingly. Right now our focus needs to be on replacing single-choice voting; the voting reform movement can figure out what the optimal voting method is as we acquire more data on how well these methods behave in actual U.S. elections. In the meantime, continue advocating for your favorite method(s), but be sure to support other reformers’ favorite methods at the same time.

This method is commonly called first-past-the-post voting or plurality voting, but I’m avoiding those terms because it’s generally not obvious what they refer to. ↩
Technically, non-monotonicity is a property of voting methods and pairs of elections, but not individual elections. However, the phrase “non-monotonic election” is often used as shorthand for “election in a non-monotonic pair of elections”, which is how I’m using it here. ↩

STAR voting in an interstate compact

2018-10-14T00:00:00+00:00

Jameson Quinn lays out a proposal for an interstate compact that links the result of the US presidential election to the national popular vote, similar to the National Popular Vote Interstate Compact. However, unlike the NPVIC, this compact is designed to support not just plurality voting, but other voting methods as well. Specifically, approval, score, and 3-2-1 are all compatible.¹ Two notable methods are missing from this list: instant-runoff voting, supported by FairVote (though under the name ranked choice voting), and STAR voting, supported by The Equal Vote Coalition.

For reasons I won’t go into here, I am more interested in STAR. Thus, I chose to work on extending the proposal to work with it. Since STAR and 3-2-1 are both rated runoff methods, I decided that it made sense to start with the procedure for 3-2-1 and modify it to fit STAR. The procedure I came up with is simply an addition to step 3 of the proposal, and works as follows:

Step 3: Possibly looking at the raw totals of other states, each state publishes its final totals. For a state using STAR, two finalists are first found by converting the raw totals into scores from 0 to 1 and selecting the two candidates with the highest average scores. Raw totals are converted as follows:

Plurality – the candidate voted for receives 1 point, and all others receive 0
Approval – approved candidates receive 1 point, and all others receive 0
Score – the minimum score is subtracted from all scores, which are then divided by the new maximum score
STAR – same process as score
3-2-1 – “good” ratings are 1 point, “OK” ratings are 0.5 points, and “bad” ratings are 0 points

Once the finalists are selected, final local totals are generated for each candidate. For each STAR ballot, 1 point is awarded to the highest-rated finalist (or both if tied) as well as any higher-rated candidates. Other candidates rated the same or lower (including the lower-rated finalist, if there is one) receive 0 points.

While step 3 was the only one to require any alterations, it was the longest step by far even before the STAR-specific instructions are added. It’s also the step that’s hardest to get right. Quinn gave a list of 4 criteria that the final local totals and the procedure that generates them should meet:

Each individual local ballot contributes between 0 and 1 points to each candidate’s final local tally.
A ballot will always contribute 1 point to its most-preferred candidate and 0 points to its least-preferred candidate.
A ballot will never contribute more points to a less-preferred candidate than to a more-preferred one.
If all states used the same final local tally procedure, the winner would be the STAR winner.²

The first criterion is obviously met since every candidate receives exactly 0 points or 1 point. The second criterion is met so long as it does not require all most-preferred and least-preferred candidates to receive the same number of points in the event of ties. The third criterion is met because all candidates receiving a score above that of the highest-rated finalist earn 1 point, and all candidates receiving a score below that of the highest-rated finalist earn 0 points. Unfortunately, the fourth criterion is not met by this procedure, as shown by this counterexample:

Number of Voters	Candidate A	Candidate B	Candidate C
1	5	5	0
1	5	4	0
2	4	5	0
4	1	0	2
4	0	1	2

Candidate A receives 22 points, Candidate B receives 23 points, and Candidate C receives 16 points, so A and B are the finalists. A is favored over B on 5 ballots while B is favored over A on 6 ballots, so B is the winner under STAR. However, the procedure I specified assigns 6 points to A, 7 points to B, and 8 points to C, so C ends up being the winner.

One thing that makes this example weird is that half the voters only rated candidates 0, 1, or 2, and thus only employed half of the available range of scores. Unfortunately, assuming all voters use the full range of their ballot does not prevent this problem:

Number of Voters	Candidate A	Candidate B	Candidate C	Candidate D
1	5	5	0	1
1	1	0	5	0
5	5	4	0	0
6	4	5	0	0
7	1	0	5	2
8	0	1	2	5

In this example, every voter rates at least one candidate 0 and at least one candidate 5. Candidate A receives 62 points, Candidate B receives 63 points, Candidate C receives 56 points, and Candidate D receives 55 points, so A and B are still the finalists. A is favored over B on 13 ballots while B is favored over A on 14 ballots, so B is the STAR winner. My procedure assigns 14 points to A, 15 points to B, 16 points to C, and 15 points to D, so under it C is the winner.

Under what circumstances does this procedure deviate from simple STAR voting? Well, the first step will select the same finalists since the ratings are altered in a way that preserves the relative differences between their sums, then added and compared as in STAR. For the second step, STAR effectively awards points to the finalists in the same way that my procedure does.³ However, unlike my procedure, STAR never awards any points to non-finalists.

Since finalists are awarded points in the same way, the finalist that loses under STAR will never win under this procedure. However, a non-finalist might win if they are higher-rated than both finalists on over half the ballots. This is because every ballot assigns a point to at least one finalist, so at least one finalist will earn points from half the ballots or more. Thus, to beat this finalist, the non-finalist will have to be rated higher than both finalists on over half the ballots, since this is the only way the non-finalist can earn points from over half the ballots. This implies that failure to choose the STAR winner is rare, since this situation should not arise often.

We can derive a couple interesting properties from this information. First of all, a non-finalist winner will necessarily beat both finalists in pairwise matchups. Since a finalist winner necessarily beats the other finalist in a pairwise matchup, this means that my procedure never elects the Condorcet loser. It also means that for 3 candidate elections, the winner under my procedure will always be either the STAR winner or the Condorcet winner. This does not hold for 4 or more candidates; in the second example I gave, D is the Condorcet winner, not C.

Of course, all of this assumes that every state is using this procedure, which implies that all states have chosen to use STAR voting. In that case, it should be easy to amend the interstate compact to simply calculate the national STAR vote if that is desirable. What’s more relevant is what happens when this procedure is used alongside the procedures for other voting methods, which is what the first three criteria cover. Thus, I chose to prioritize meeting them over the last criterion.

Overall, I feel this is reasonable for a first version of an extension of Quinn’s proposal to STAR voting. Given the assessment I was able to provide, I see no reason why this procedure would behave badly. It converts STAR ballots to scores of 0 or 1 in a way similar to how 3-2-1 ballots are converted, and while it can’t guarantee the STAR result within the states that use it, it can only fail to give the STAR result when another candidate is rated higher than the two finalists on over half the ballots, an event which should be rare.

It also works with borda count, but because borda is (at least arguably) worse than plurality, I have chosen to omit it. ↩
Since Quinn was applying the criteria to the tally procedure for 3-2-1 voting, this originally said “the 3-2-1 winner”. ↩
It’s probably more accurate to say that STAR awards 0 points to both finalists for ballots where they are tied, but saying it awards 1 point to both like my procedure does will never change the outcome, so I ignore this for simplicity. ↩

Should you pursue common or rare achievements?

2018-07-21T00:00:00+00:00

Recently I’ve been considering what video game achievements are most worth aiming for. Specifically, the question is whether I should go after common achievements or rare achievements. I’d been targeting rare achievements, but it occurred to me that I might be better off going after common ones instead.

One reason to pursue common achievements is that they’re generally lower-hanging fruit. All else equal, the easier an achievement is, the more people will have it. Thus, if you simply want to maximize the number of achievements you have, going after more common achievements seems like the way to go. Occasionally a rare achievement may seem just as easy, but that shouldn’t be your main focus, only a possibility that you pursue as it comes up.

Another factor to consider is the potential embarrassment of not having a particular achievement. Lacking a common achievement could be very embarrassing. After all, if an achievement is held by 80% of the player base, then how come you don’t have it? On the other hand, lacking a rare achievement is much more understandable. Unless you’re a huge achievement hunter, no one will be surprised that you’re missing an achievement that less than 1% of all players have. Being embarrassed over not having an achievement does seem like a rather unlikely scenario, but it’s always possible that a friend may want to compare achievements or something, so it is a factor worth considering.

While common achievements may be better when someone is looking through all your achievements, rare achievements are nice when you can direct attention to a specific set of achievements. Steam is a major video game platform that allows you to do just that, offering both a general achievement showcase option and a rarest achievement showcase option for player profiles. Rare achievements will generally be more impressive than common ones, so if you’re looking to show off what you’ve achieved, focusing on rare achievements seems like the way to go.

If you’re unconcerned with what others think, you may still want to target rare achievements because of the satisfaction you feel upon achieving them. This will obviously vary from person to person, but it’s likely that common achievements don’t feel as special to complete since so many other people have already acquired them. It’s generally much more satisfying to accomplish something that few others have. Therefore, if others’ opinions of your completed achievements don’t bother you but you do care about the satisfaction of obtaining rare achievements, focusing on those rare achievements appears to be a good idea.

After considering these arguments, I decided that going after rare achievements was still the best decision for me. I don’t think I care about quantity too much, and I don’t expect to be embarrassed about missing common achievements. In contrast, I can choose to show off the rare achievements I have, and acquiring them is a rewarding activity for me. While I don’t expect this to be the best option for everyone, I am reasonably confident that I have made the right decision.

Why discuss superintelligence?

2018-07-01T00:00:00+00:00

My site now contains a miscellaneous section with exactly one page, the Superintelligence reference page. I’ve briefly brought up superintelligence in the past, but I’ve never discussed it in detail. However, given that others have already written so much about it, I feel like it makes more sense to collect the resources I think do a good job of explaining it. Therefore, if you have no idea what superintelligence is or why you should care about it, I’d recommend starting with some of the links in the Introductions section before reading on.

You back? Good. At this point, you might be wondering why I’ve singled out this topic as one worth prioritizing. The answer to that question is that superintelligence is an existential risk. Using a conservative estimate, it is possible for humanity to create 10³⁴ fulfilling years of human life throughout the remainder of the universe’s existence. Thus, ensuring humanity remains capable of doing so is extremely important. This and other concerns justify treating existential risk prevention as a global priority.

Because superintelligence is an existential risk, ensuring that it is aligned with human values is a very important problem. Some organizations even consider it to potentially be the most important global problem that humanity has identified thus far. At the same time, media coverage of this issue and AI in general has been increasing, and a lot of it is not very good. Therefore, it seems important to have resources available on the subject.

As of this post, the reference page has only three sections, but I plan to expand upon it in the future. Topics that I plan to add include the orthogonality and instrumental convergence theses, the intelligence explosion concept, and scenarios without an intelligence explosion. There’s a lot of room to grow the page, and I think doing so is definitely worthwhile.

My thoughts on Microsoft acquiring GitHub

2018-06-04T00:00:00+00:00

Today it was announced that Microsoft is acquiring GitHub. The responses to this event have been mixed, with some people expressing optimism and others fear. I have two lines of thought regarding this subject.

First of all, I don’t expect Microsoft to ruin GitHub. I agree with those who believe that Microsoft genuinely cares about open source. So long as software is a complement to Microsoft’s products, Microsoft is incentivized to support open source software. I was worried when I discovered that Microsoft’s revenue from Windows is dropping since operating systems are an obvious complement of software, but luckily Microsoft seems to be pivoting to cloud services, another complement of software. Therefore, I expect that Microsoft will at least avoid damaging GitHub in any way since it stands to gain from open source.

What does worry me is the larger pattern that this acquisition is a part of. Microsoft has made a lot of acquisitions in the past, and it’s far from the only company to do so. This pattern, along with some other factors, has resulted in a major increase in market power, which means there’s a lot less competition among companies. This leads to a variety of problems, including lower wages, less economic growth, and the phenomenon known as cost disease, among many others. So while I don’t think there’s anything wrong with this acquisition specifically, in context it is part of an extremely harmful pattern that needs to be ended.

Outlining the opposite of a singleton

2018-06-01T00:00:00+00:00

In one of my previous posts, I discussed the concept of a singleton as defined by Nick Bostrom. Now I’d like to consider what the rough opposite of a singleton would look like, based on what has been written by others on the subject.

For me, the obvious place to start is Scott Alexander’s Meditations On Moloch. In it, Moloch is introduced as that which causes the following:

In some competition optimizing for X, the opportunity arises to throw some other value under the bus for improved X. Those who take it prosper. Those who don’t take it die out. Eventually, everyone’s relative status is about the same as before, but everyone’s absolute status is worse than before.

This type of situation is known as a coordination problem, something I discussed previously in the context of boycotting video games. If those in the competition could choose to cooperate, they could easily coordinate to avoid sacrificing any other values. But as long as they are competing, once one of them chooses to sacrifice something for a short-term advantage, the rest must do the same or be eliminated.

Note that in less intense competitions with fewer participants, there’s a greater chance that no one will take the first step, allowing values that could be traded away to remain. Total coordination failure would involve a large number of entities competing, enough that any opportunity to trade away a value is taken almost immediately.

As enlightening as I find this post to be, it does not identify the opposite of a singleton. Moloch is the force that might lead to this opposite manifesting, but it is not the opposite itself. In order to find that, we will have to look elsewhere.

Where should we look? Well, we know that if the opposite ever manifests, it will be because of Moloch. Thus, a “competition optimizing for X” will be involved. But what X are we looking for? It needs to be something fundamental, something that isn’t destroyed even if civilization is eliminated and the world is nothing but chaos. And what is more fundamental for agents in a competition than existence itself? It’s not like you can even participate in a competition if you don’t exist in the first place. The answer, it would seem, is survival.

But it’s not quite that simple. Take evolution, for example. Survival is actually not its most important component; reproduction is. Now if one holds reproduction as their terminal goal, survival does happen to be a key instrumental goal. However, it is safe to say that evolution is a competition optimizing for reproduction. After all, if evolution were a competition optimizing for survival, then it would be weird to find that most species could die of old age. In contrast, all species are capable of reproducing, so reproduction fits the bill much better.

This leads us to our next major source, Wireheading Done Right: Stay Positive Without Going Insane. Most of this post is actually not relevant to our discussion, but this paragraph is an exception:

I will define a pure replicator, in the context of agents and minds, to be an intelligence that is indifferent towards the valence of its conscious states and those of others. A pure replicator invests all of its energy and resources into surviving and reproducing, even at the cost of continuous suffering to themselves or others. Its main evolutionary advantage is that it does not need to spend any resources making the world a better place.

The given definition, while useful in its original context, is oddly focused on what a pure replicator doesn’t do. The sentence that follows is much more important to us. A pure replicator focuses solely on surviving and reproducing. Keeping in mind that survival is merely an instrumental goal, I will redefine a pure replicator as an agent that optimizes for its own reproduction.

Now that we have this concept, we can finally get around to naming and defining the opposite of a singleton. I have chosen to name this concept a replicator world. I define a replicator world as a world order in which all highest-level agencies are pure replicators.

Let’s break this new definition down. First of all, a replicator world is a world order just as a singleton is. Both are incompatible with all other world orders, as world orders extend throughout their domain and do not leave room for anything else.

Next, we need to know what a highest-level agency is. Agencies are able to combine with each other to form a new agency, which is considered to be one level higher than the agencies forming it. For example, cells can be thought of as agencies that come together to form higher-level agencies called multicellular organisms. A highest-level agency is an agency that is not part of any higher-level agency. In the case of a singleton, the singleton itself is the only highest-level agency, and all other agencies are a part of it. In the case of a replicator world, there are many different highest-level agencies.

Finally, all those highest-level agencies have to be pure replicators. It’s important that this condition be restricted to agencies at the highest level because pure replicators are bad at forming higher-level agencies thanks to the free-rider problem. When agencies form a higher-level agency, they do so because they expect to benefit from it. However, if an individual agency chooses not to contribute to the effort, it will still receive the vast majority of the benefits from the higher-level agency despite experiencing a much lower cost. There are solutions to this problem, but they tend to involve other values that a pure replicator will immediately trade away for an increased ability to reproduce. Thus, highest-level agencies that are pure replicators will likely consist of agencies that aren’t pure replicators. For example, an organism that functions as a pure replicator may be composed of non-cancerous cells that do not function as pure replicators. This justifies restricting the condition of being a pure replicator to highest-level agencies.

One feature of replicator worlds is that, shortly after their creation, they will always be roughly at their carrying capacity. This occurs because agencies optimizing for reproduction will initially use up excess resources at an exponential rate as their population grows. While the logistic model suggests that growth will slow down again as the population approaches the carrying capacity, by the time growth has been substantially slowed the population will already be roughly at the carrying capacity.

This in turn implies that agencies in replicator worlds will have access to almost no resources beyond those necessary for survival, as carrying capacity is the population size in which all resources are used simply for survival. While it is almost certain that replicator worlds will expand to gain access to additional resources, any time pure replicators come upon excess resources they will immediately begin reproducing until there are enough offspring that all resources are used solely for survival, restoring the population to carrying capacity. This will likely occur fast enough that no agency will have access to a significant amount of excess resources at any point in their existence.

From this, it can be deduced that replicator worlds experience little to no technological development. All agencies have to choose between exploration and exploitation, a dilemma known as the explore-exploit tradeoff. However, agencies in replicator worlds are strongly incentivized to exploit any resources they have rather than use them for exploration. Most of the time they will only be able to survive if they exploit all their resources to that end. Even at times when they have excess resources, however, pure replicators will want to use them for reproduction. While exploration could yield results that help a pure replicator by, for example, increasing how efficiently it can use resources, this sort of discovery takes time, time an agency in a replicator world will likely not have. Other agencies are seeking out resources as well, and once the excess resources are gone the easiest resources to obtain may be the ones being used for exploration.

If exploration is this unrewarding, agencies will likely sacrifice the ability to explore at all. If doing so gives agencies even a slight advantage in resource usage, this move could very well make sense in such an intensive competition. Interestingly, such a modification would be the last one an agency makes, as modifications are inherently a form of exploration.

Another feature of replicator worlds is a lack of coordination at the highest level. This should be expected, as a singleton has everything coordinated by one agency. Several major implications result from this. One is that no governments or other organizations comprised of highest-level agencies will exist. Organizations are dependent on coordination between their members, but this will not be possible in a replicator world. In fact, since an organization would actually count as a higher-level agency, it is by definition impossible for an organization to be formed from highest-level agencies. Thus, there are only two possible ways that something like a government could exist in a replicator world: either it must be a pure replicator, or it must be a lower-level agency within a pure replicator.

Another implication is the lack of an economy or any looser means of coordination among highest-level agencies. While these forms of coordination may not be tight enough to form higher-level agencies and therefore do not suffer from a definition issue, they are nonetheless dependent on a process that cannot happen between pure replicators. As such, they can only possibly appear in a replicator world if they can exist within a pure replicator.

I believe that this outline of a replicator world effectively captures what I would intuitively expect the opposite of a singleton to look like. However, this by no means implies that it is correct. I expect to at the very least significantly alter my conception of this concept as I think about it more. However, I am quite happy with this as a first attempt to tackle understanding this area.

Freedom of speech is good

2018-05-20T00:00:00+00:00

In my previous post, I laid out what I consider to be the strongest argument against freedom of speech. Now I will cover what I believe to be the flaw in that argument.

In that argument’s analogy, ideological propaganda produced by think tanks is equated with pathogens produced by bioweapon labs. But this comparison misses something. Multiple pathogens will all weaken a host more than just one of them would, but multiple ideologies will contradict and weaken each other, influencing people less. This gives freedom of speech an advantage that “freedom to distribute pathogens” lacks.

When freedom of speech is eliminated, it is generally done so by one group that chooses to allow its own speech but bans that of other groups it opposes. Thus, one set of think tanks continues to distribute their ideology, but the others are no longer able to do so. This allows the favored ideology to have a greater impact on people than the spread of all ideologies would’ve. If one bioweapon lab banned all the others from distributing their pathogens, it would be an improvement; this does not hold true for think tanks and ideologies.

This doesn’t imply that freedom of speech and the marketplace of ideas automatically lead to the truth, but it does suggest that they are components of a system that does. Without freedom of speech, it’s much easier to entrench false ideas within society. Creating a marketplace of ideas at least puts some pressure on ideas to be truthful. However, some additional mechanism is necessary to ensure that more truthful ideas are believed and spread more. Otherwise, the marketplace of ideas, which directly optimizes for ideas that are believed and spread, ceases to indirectly optimize for truth.

I don’t know what such a mechanism would look like, but developing one seems like it could become more important as the power of propaganda increases. In the meantime, defending freedom of speech ought to help. It won’t solve the problem, but at the very least it should slow down the rate at which the situation deteriorates.

Freedom of speech is bad

2018-04-28T00:00:00+00:00

I consider freedom of speech to be one of the most important foundations of today’s society. However, in this post I’d like to present what I believe is the strongest argument against free speech, then follow it up with the reason I think said argument is wrong in a later post.

The groundwork for this argument (though certainly not the argument itself) is laid out in detail in Scott Alexander’s Meditations On Moloch, which I recommend you read first. The most relevant part is as follows:

The point is – imagine a country full of bioweapon labs, where people toil day and night to invent new infectious agents. The existence of these labs, and their right to throw whatever they develop in the water supply is protected by law. And the country is also linked by the world’s most perfect mass transit system that every single person uses every day, so that any new pathogen can spread to the entire country instantaneously. You’d expect things to start going bad for that city pretty quickly.

Well, we have about a zillion think tanks researching new and better forms of propaganda. And we have constitutionally protected freedom of speech. And we have the Internet. So we’re kind of screwed.

The obvious way to solve the problem in the analogy is to remove the right to exist and contaminate the water supply that the bioweapon labs currently possess. The other apparent option, eliminating the mass transit system, is both less effective, since the pathogens will merely spread at a lower rate, and more costly, since the mass transit system is otherwise a very useful innovation.

The implications of this are troubling. The problems with eliminating the mass transit system appear analogous to problems with eliminating the Internet. Eliminating freedom of speech also seems like it would be more effective, so the only part of the analogy that remains to be upheld is the lower cost.

This is the point where the marketplace of ideas will be brought up to justify keeping freedom of speech. Allowing ideas to compete so that the truth may come out on top makes freedom of speech very beneficial, and thus much more costly to remove than the analogous rights of the bioweapon labs. Unfortunately, another point made by Scott Alexander suggests that this is a weak argument:

Memes optimize for making people want to accept them and pass them on – so like capitalism and democracy, they’re optimizing for a proxy of making us happy, but that proxy can easily get uncoupled from the original goal.

Chain letters, urban legends, propaganda, and viral marketing are all examples of memes that don’t satisfy our explicit values (true and useful) but are sufficiently memetically virulent that they spread anyway.

So the marketplace of ideas is not actually as valuable as it may seem. After all, think tanks wouldn’t be that large of a threat if it were; their ideas would simply be outcompeted by the truth. This implies that the cost of eliminating free speech is not that high, and thus that doing so is the correct solution.

Next post will be an explanation of where I think this argument breaks down.

Comic Sans is a great font

2018-04-01T00:00:00+00:00

Everyone loves to hate on Comic Sans. Even those who know nothing about typography will spend the time to go on long rants about how awful it is. But the truth of the matter is entirely different from what common knowledge suggests. In reality, Comic Sans is a great font.

What makes Comic Sans so great? For one thing, it’s an easily recognizable font. It was originally released as one of five fonts supplied by Windows 95. This allowed it to spread very quickly as many personal computer users employed it in their printouts. The intense hatred that many hold for it only renders it even more recognizable. For them, Comic Sans is the enemy, and an inability to identify your enemy leads to a swift defeat. Thus, the Comic Sans haters cannot help but fuel its recognizability.

Comic Sans is also often preferred by those with dyslexia. While it is not a specialized font and therefore does not perfectly fulfill this role, it does a much better job than practically any font the Comic Sans haters will hold up. Very few fonts can match the legibility and letter spacing that Comic Sans brings to the table. It does contain mirrored letters which allow specialized fonts to surpass it, but giving those up trades away consistency, which can be very distracting for other readers. Comic Sans does an excellent job of balancing other concerns with accessibility for dyslexic readers.

One common complaint against Comic Sans is that it is an informal font often used in formal contexts. As long as the uninformed make use of it in documents in which the informal tone it sets is inappropriate, its very existence is detrimental, or so the argument goes. However, this fails to take into account the concept of countersignaling. Countersignaling is when you communicate that you strongly possess a property by not making it more conspicuous. For example, those who are newly rich will likely flaunt their wealth to make it clear that they are no longer part of the middle class, but those who are already known to be rich will worry about differentiating themselves from the newly rich, and will accomplish this by not flaunting their wealth. This only works because they are not afraid of being mistaken for a member of the lower or middle classes. That’s the reason countersignaling even works: you must be so confident in the trait you are countersignaling that you are willing to avoid emphasizing it because you know others will pick up on it anyway.

In the case of Comic Sans, many formal documents are very obviously formal regardless of the font. For instance, a doctor’s diagnosis is unlikely to be mistaken for something informal, and thus it is possible to get away with countersignaling. In fact, in basically every case in which you can tell that an informal tone is inappropriate, countersignaling is a viable strategy. So if you really want to emphasize your formality in such an instance, don’t use some standard formal font. Use Comic Sans.

But if Comic Sans is such as great font, why does everyone seem to hate it? The answer to that question lies in the history of graphic design and the rise of the internet. Early personal computers dramatically reduced the cost of high quality print design, and colleges began to produce a much larger number of graphic design graduates. However, personal computers also put the power of graphic design into the hands of everyone who owned them. While most people were slower to figure out they had this power than the graphic design students were, they did eventually learn. This was only the first step in the reduction of graphic designers’ power.

The second, far more dramatic step was the growth of web design. As print design began to die off, designers had to learn to code just to retain relevance. This made them understandably bitter, and they took their anger out on those performing graphic design without a degree. And what font did these amateurs with personal computers happen to be using? That’s right: Comic Sans. This made the font an obvious means of defining an ingroup and an outgroup. If you liked Comic Sans and used it a lot, you were a useless pretender who lacked even the most basic design knowledge. But if you hated Comic Sans, then you were a sensible designer who understood how things actually worked. Thus, hating Comic Sans was associated with understanding graphic design, and anyone who wanted to not look like an idiot learned to avoid it.

Well, I say enough is enough. It’s time to take Comic Sans back from the elitist graphic designers who use it as a symbol of their superiority. If you have a website, switch it over to Comic Sans. If you design documents, start writing them in Comic Sans. In every situation in which you get to choose the font, choose Comic Sans. Together we can retake this wonderful font from those who have abused it for so long!

How to win The Game

2018-03-14T00:00:00+00:00

For anyone who has no idea what the title is referring to, The Game is a mental game with three simple rules.

You are playing The Game.
Every time you think about The Game, you lose.
Loss of The Game must be announced.

These rules lead to a meme that propagates itself without generally providing value to the minds it inhabits. Everyone is either not thinking about The Game, in which case it has no effect on them, or thinking about The Game, in which case they are losing it. However, it is possible for some people to get utility out of this.

By spreading this meme to other minds, those that enjoy watching others lose can benefit from what is otherwise a detrimental meme. However, this is a negative-sum game, so it is still harmful to the group as a whole. This means that while it is possible for a few trolls to benefit, it would still be best if The Game didn’t exist. Unfortunately, it is intentionally designed such that it cannot be ended. Winning is simply impossible.

All that means is we need to get a little creative. If something you want to accomplish is impossible, your next goal should be to try to merely approximate that thing. For example, literally defying gravity is, to the best of our knowledge, impossible. There is no way to just ignore it. However, this does not prevent airplanes and rockets from working. While they do not literally defy gravity, they do a good job of approximating what defying gravity would look like. Likewise, we want to approximate how winning The Game would appear.

In order to do so, we first need to establish what that approximation is like. Our goal is to end a negative-sum game. Thus, an important property we’re looking for is that The Game no longer reduces total utility. If we can accomplish this, then we will have approximated winning The Game well enough for our purposes. The problem is that we cannot just modify The Game to have the desired properties. This means our only option is to create something new. If we want to prevent total utility from being reduced, we’ll have to increase total utility, which will require the creation of a positive-sum game. Furthermore, this positive-sum game should provide utility whenever The Game reduces it so as to better approximate The Game’s nonexistence.

I now present my solution to this task: The Meta-Game.

You are playing The Meta-Game.
Every time you think about The Game, you win The Meta-Game.
Winning The Meta-Game must be announced.

The first rule ensures that The Meta-Game applies to everyone The Game applies to. The second rule directly combats the negative-sum nature of The Game by making The Meta-Game a positive-sum game that awards players on the exact condition that causes them to lose The Game. The third rule helps The Meta-Game spread in the same way The Game spreads.

You might notice a problem here. Sure, players win The Meta-Game at the same time they lose The Game, but does the win really cancel out the loss? After all, doesn’t the utility gained or lost depend on how much you actually care about The Game vs. The Meta-Game and winning vs. losing? While this could be a problem in some cases, I think it can be reduced to a nonissue for most people. Remember that The Game is usually brought up by those who enjoy making others lose it. Most people will probably enjoy foiling the trolls’ plans quite a bit, so they should at least break even on utility, if not gain some.

Even this reasoning is not quite perfect, though, as it is actually circular. You have to defeat the troll in order to gain the utility that allows you to defeat the troll. This can be solved by having the troll be gradually defeated over multiple wins. Initially, they are only defeated a little bit thanks to the utility gained simply by winning a game. The next time The Game is lost, utility is gained both from winning a game and from knowing that the troll will be partially defeated, as they were last time. The third time, even more utility is gained thanks to the increased success at defeating the troll the previous time. This process continues indefinitely, and the utility gained from every time The Meta-Game is won will converge to the amount we previously arrived at circularly. (It is reasonable to assume convergence here since divergence would imply that winning The Meta-Game enough times would allow an arbitrarily large amount of utility to be gained upon every further win.)

If you followed all that and agreed with it, then congratulations, because you have just won The Game and therefore become invulnerable to it. Please be sure to use your newfound powers responsibly and spread The Meta-Game anywhere The Game has taken root. If you didn’t follow that or you disagree with my reasoning, I welcome you to leave a comment asking questions or arguing against this.

Arguing over definitions

2018-03-08T00:00:00+00:00

I recently got into an argument involving topics like whether water was wet and whether hotdogs were sandwiches. What all the topics had in common was that they were not arguments over facts but rather arguments over definitions. This means there is nothing in observable reality that can be pointed to in order to resolve them. What’s worse is that many arguments will fall into this category by default.

The problem is that until all relevant definitions are agreed upon, an argument will often not be about facts. As long as one definition isn’t agreed upon, the participants can make two different statements using the same exact words, which is terrible for communication. If “a hotdog is a sandwich” is interpreted by one person as “a hotdog is meat on bread” and by another person as “a hotdog is meat between two pieces of bread”, they may both think the other person is crazy. If they realize that the dispute is really over definitions, they may still believe that it is unreasonable to use any definition besides the one they use.

Is there a way to resolve this type of dispute? I would argue that it makes the most sense to debate how practical the definitions are. This includes how observable they are and how useful they are. For example, it’s pretty simple to observe if a hotdog has meat on bread. However, it may be a little harder to tell how many pieces of bread there are, such as when the bun is either split in two or almost split in two. These states are similar enough that observing the difference can take extra effort, penalizing definitions that distinguish between them.

However, what matters more than how difficult the required observations are is how useful those observations are. If distinguishing between one piece of bread and two pieces of bread is important, then it hardly matters if doing so takes a little more effort. However, barring something like cultural significance, this distinction does not seem useful, so the observation difficulty wins out (at least in my opinion). On the other hand, if someone attempted to define the word dignity as a category consisting of rocks, rockets, and cats, their definition would probably be judged as inferior to the standard definition. While it is easier to observe those things than it is to observe an abstract concept like dignity, the standard definition is simply much more useful and thus wins out.

The problem with this approach to resolving definition arguments is that it merely attempts to transform them into factual arguments. If the definitions relevant to determining which definition is more practical are also not agreed upon, you end up with a case of infinite recursion. At the end of the day, language is a fundamentally imprecise tool for communication. It’s very useful and works quite well, but it’s not perfect. As of now, though, it’s the best thing we’ve got.

How intelligent are we?

2018-03-02T00:00:00+00:00

Humans are generally thought of as the most intelligent beings to exist, as we have discovered nothing that appears to be more intelligent than us. But how intelligent are we compared to the theoretically attainable maximum? I believe that we are far less intelligent than is physically possible. This is because we possess roughly the minimum level of intelligence necessary to create a technological civilization.

To understand why this is so, we must look at how we came to have this level of intelligence in the first place. Over a period of about 50 million years, the brains of rat-like creatures evolved into the brains of chimps. This was a complex process that involved major structural changes. However, going from chimp brains to human brains only took about 5 million years and required only minor changes to brain structure, suggesting a faster but more gradual process that was unlikely to end at the exact time civilization started. So if one were to ask the question of why we stopped at our current level of intelligence, I would argue that we haven’t necessarily. Instead, we’re at this level because it allowed us to begin building civilization, a process that occurs on a much faster timescale than evolution.

The Agricultural Revolution occurred roughly 12,000 years ago. Since then, humanity has done all sorts of crazy things involved in building civilization, including at least one other major technological revolution, while evolution has only had time to make the most minor of changes. Thus, while there may still be room for evolutionary pressures to improve primate intelligence in the same way it’s been improving for the past 5 million years, the 12,000 years over which civilization has existed are simply too small for noticeable progress to occur. If a lower level of intelligence enabled the creation of civilization, then it would’ve moved too fast for us to be able to observe it in its current state with our current level of intelligence. Thus, whatever level of intelligence we observe ourselves to have from within a civilization is roughly the minimum level of intelligence capable of giving rise to that civilization.

This in turn suggests that there could be much more room for our intelligence to grow. It seems unlikely that the minimum level of intelligence that enables civilization would also be the maximum level of intelligence enabled by the laws of physics. Thus, I propose that humans are likely well below the theoretical maximum intelligence level.

Whether we are close to maximum intelligence is important for several topics. Brain-machine interfaces are much more important if there is significant room for them to augment our intelligence. Superintelligence is a greater concern the further we are from maximum intelligence. A distant maximum intelligence also leaves room for technologies like genetic engineering to possibly enhance human intelligence in the near-term. If these are all possible, then we would be wise to prepare for them ahead of time.

Singletons and universal inevitable threats

2018-02-09T00:00:00+00:00

One concept I find particularly fascinating is that of the singleton. As defined by Nick Bostrom, a singleton is “a world order in which there is a single decision-making agency at the highest level”. He states that such an agency would have “the ability to prevent any threats (internal or external) to its own existence and supremacy”. However, it is not at all obvious to me that this is true. To crystallize my intuition I would like to introduce my own concept: the universal inevitable threat.

An inevitable threat is defined as a threat that eliminates an agency regardless of the actions that agency takes. This leaves open the possibility of delaying the threat for a finite period of time, but beyond that, the agency may only choose how to spend the time it has prior to the threat’s realization. It can neither eliminate the threat nor hold it off indefinitely.

A universal inevitable threat is then defined as an inevitable threat that applies to all possible agencies. A notable property of such a threat is that it cannot be brought about by an agency, as this would imply that the agency had a course of action that would result in the threat not occurring and therefore that the threat was not inevitable relative to that agency. This concept is relevant because if a universal inevitable threat exists, then no agency is able to prevent all threats to itself, including a singleton. Furthermore, several plausible candidates for a universal inevitable threat can be identified.

The first possibility is simply the end of the universe. Exactly how the universe will end has yet to be determined, but most hypotheses posit scenarios that appear to be universal inevitable threats. One example is the heat death of the universe, which would result in a state of maximum entropy in which no information processing can take place. Since information processing seems to be essential for agencies to operate, this scenario would count as a universal inevitable threat.

Another potential end of the universe is the Big Rip scenario. In this case, the universe’s increasing expansion rips everything apart into elementary particles and radiation. Unless an agency can somehow develop a way to survive the infinite expansion rate that is eventually reached, all agencies are eliminated, making this a universal inevitable threat.

The Big Crunch is yet another possible end state of the universe. This possibility involves the universe collapsing into a dimensionless singularity. A related scenario is the Big Bounce, which follows the Big Crunch with another Big Bang to create a cycle. Unless some agency can survive a singularity of infinite density, both cases are universal inevitable threats.

Another category of universal inevitable threat candidates is resource depletion scenarios. Some scenarios for the end of the universe can actually be framed as falling under this category. For example, heat death can be viewed as the universe running out of negentropy. However, it is possible that some other resource is both essential for agencies to function and depleted prior to the end of the universe. The depletion of such a resource would be a universal inevitable threat.

The final category of candidates for universal inevitable threats is that of naturally occurring physics disasters. An example of this would be false vacuum decay. If the universe is currently part of a metastable vacuum, it could be disrupted, creating a bubble of lower-energy vacuum that expands at the speed of light. This could fundamentally alter the universe in such a way as to destroy any agencies in existence prior to the event. False vacuum decay and any similar physics disasters that occur naturally would likely be universal inevitable threats.

While it is not yet possible to confirm the existence of a universal inevitable threat, there does seem to be a significant probability of one existing. In particular, the end of the universe is very likely to be one. If one exists, it would prove that no agency is able to prevent all threats to itself, and thus that singletons do not possess this power, as seems probable to me.

Colonizing Mars does not mean abandoning Earth

2018-02-04T00:00:00+00:00

Colonizing Mars is often talked about in the context of preventing the extinction of humanity. This has led to the unfortunate misconception that colonization results in the abandonment of Earth. I’d like to take the time to explain why this doesn’t happen.

Before we explore just why Earth wouldn’t be abandoned, it will be useful to review the extinction risk argument for colonizing another planet. The argument starts by noting that out of all species to ever live on Earth, 99.9% have gone extinct. It then goes on to point out how most of these extinctions occurred in planet-wide events called mass extinctions. Thus, establishing a species on another planet would be a good way to increase its chances of survival. If a cataclysmic event wipes the species off one planet, it is simply a matter of waiting for the dust to settle before reintroducing them from the other planet.

One detail of this plan is extremely important: so long as no such event has occurred, it is essential that the species be well-established on both planets. Once the species is wiped off one planet, it becomes as vulnerable as it used to be until its presence on that planet is restored. Abandoning the species’ home planet in favor of a newly colonized one thus completely fails to increase the species’ survival rate.

The misconception stems from the idea that once Mars is colonized, Earth will become unnecessary to the survival of the human race. Since the end of humanity on Earth no longer means the end of humanity, we are free to abandon it whenever we want. But this ignores that the whole purpose of colonizing Mars was to have two planets instead of one. Mars may be essential to the plan, but so is Earth.

But won’t having Mars as a backup mean we put less effort and resources toward preventing a catastrophe on Earth? No, because there will still be plenty of people living on Earth, and their lives will be as valuable as ever. Humanity will be wiped off the face of the Earth only if no way exists to prevent it.

However, if Mars is colonized, then Earth can actually be re-inhabited, given enough time. Therefore, colonizing Mars is actually the opposite of abandoning Earth; it is a means by which to remain on Earth. That is why many people see it not as the abandonment of our home, but as an important step to take for protecting both it and humanity.

Can boycotts be solved?

2018-02-01T00:00:00+00:00

In my last post, I talked about why individuals’ incentives will prevent video game boycotts from succeeding. Now I’d like to discuss potential solutions (or at least vague outlines for potential solutions) to this problem.

The first idea that comes to mind is looking at historical successes. Two successful boycotts that I’m aware of are the Continental Association and the Montgomery bus boycott. For those who don’t know, the Continental Association was a boycott of British goods by the American colonies prior to the American Revolutionary War, and the Montgomery bus boycott was a protest against the segregated bus system in Montgomery, Alabama during the American Civil Rights Movement. In looking at these examples, I hope to identify both parts of a coordination mechanism: an agreement and an enforcement mechanism.

The Continental Association’s agreement is easy to find. The Association’s articles stated that colonists would refuse to import British goods and American merchants would avoid price gouging to ease the resulting burden. Likewise, the articles provide several enforcement mechanisms. Those violating the agreement were to be publicly ostracized and condemned. Committees of inspection were set up to monitor businesses. Colonies had to cease all dealings with any colony that did not comply. Additionally, violence was employed to force compliance on some occasions. These mechanisms were successful enough for all but one colony to comply up until the war began.

The Montgomery bus boycott also has a simple agreement. The buses would not be ridden until the city agreed to switch to a compromise between the current rules and desegregation. The enforcement mechanism is less obvious, but given the strength of the black community and its churches, it’s reasonable to assume it was social pressure. Community members often helped each other out, and losing that support could be devastating, so if the community said you should join the boycott, you probably joined the boycott. Similarly to before, this was enough for the boycott to last until the United States Supreme Court ruled segregation on public transportation illegal.

Coming back to video game boycotts, the agreement seems easy to create. Refuse to purchase the game until the game’s publisher stops whatever prompted the boycott. The difficult part is the enforcement mechanism. The Continental Association’s methods don’t seem particularly helpful. Committees of inspection could be ignored, no obvious analog to colonies exists, and violence is a poor solution for most problems. That leaves social mechanisms, the strategy that was also employed for the Montgomery bus boycott. This is probably the most plausible option, but it’s still pretty bad. The online disinhibition effect weakens social restrictions, reducing the chances that an online community will be able to pressure its members into coordination. Therefore, I think it would be wiser to look at other options.

The most powerful coordination mechanism ever created by civilization is probably government. In a government with legislative and executive branches, the legislative branch sets the agreements while the executive branch enforces them. Thus, one way to solve our problem is to get a law passed that bans the targeted activity. Then everyone is forced to “boycott” offending games by means of their nonexistence.

Of course, this idea is not without its problems. First of all, you need to grab the attention of your legislators while thousands of other causes also vie for their attention. Next, you need to convince them that supporting your law is in their best interests, even though there will almost certainly be objections and proposals for changes that no one will agree on. Additionally, you need to actually have a law for them to support. If you can’t specify the activity that needs banned well enough, your law will either be ineffective or ban actions that should be allowed. This brings up another problem, which is that your law restricts the freedom of others. If some people don’t mind a game with the opposed features and your law prevents it from being made, your actions may become rather questionable.

Perhaps we need to think outside the box more. In Inadequate Equilibria, Eliezer Yudkowsky mentions the idea of a timed-collective-action-threshold-conditional-commitment, essentially a generalized version of Kickstarter, as a means to coordinate action. In our case, the idea would be to have potential boycotters agree to the boycott if and only if a certain number of other people also agree to it. The problem is that there remains a need for an enforcement mechanism. In Kickstarter’s case, backers pay when they make the agreement and their money is returned if the project fails to meet its funding threshold. Thus, backers don’t have the option to not pay, but must instead trust the company to not keep the money for a failed project. A similar solution might work for boycotting video games, though there are multiple challenges to overcome.

First off, participants need to have not already bought the game. If those who have purchased the game are allowed to appear to participate, then we will once again end up in a situation where no one is incentivized to actually participate. For the same reason, participants must be incentivized to avoid purchasing the game in the middle of the boycott. We also want to ensure that all participants are actually interested in buying the game being boycotted so the publisher is incentivized to meet the boycott’s demands.

Taking this into account, here is my rough proposal for a Kickstarter-like boycott company. A boycott agreement would have participants deposit enough money to buy the game being boycotted. After a set time, if a set number of people has not been reached, the deposit is returned and no obligations remain. However, if the set number of people is reached prior to the set time, the boycott begins. At this point, any participant who buys the game will lose their deposit. Those who don’t buy the game will have one of two things happen to their deposit. If the boycott is judged successful, their deposit is used to purchase the game for them. However, if a set duration passes without the boycott being judged successful, the deposits are returned. Alternatively, they could be put towards purchasing a similar game by a rival publisher.

Why use something like this structure? The deposit is important because it serves as the enforcement mechanism. If you fail to remain in the boycott, you lose money. A successful boycott leads to the deposit buying the game for two reasons. First of all, it provides an incentive not to buy the game prior to the end of the boycott even if you could do so without being detected (such as by using an alternate account), since you’ll end up getting two copies of the game if it succeeds. It also helps discourage people who don’t care about the game from participating, which is important if they are otherwise incentivized to.

The reason such people might be incentivized to participate is that the deposits of anyone who buys the game during the boycott might be redistributed to those who didn’t buy it. This would create an opportunity for profit that might be exploited. Other ways to prevent this include forcing deposits to be put toward another game upon a failed boycott or letting the company running the boycott keep the forfeited deposits as extra profit. The first option has the advantage of reducing the chance that participants buy the game after the boycott is over, which makes the boycott more credible to the publisher. However, it may discourage people from participating since their control over the money they deposit is vastly reduced. Letting the boycott company keep the deposits has the drawback of incentivizing the company to have some people buy the game during the boycott.

There are still plenty of problems with this design, and I’m sure that, if it is not entirely useless, it would at the very least need to undergo several rounds of improvement to actually be viable. But it would be very interesting if a company loosely resembling this proposal arose one day. In the meantime, there is one last idea I’d like to take a look at.

Instead of using a boycott, we could instead treat the desired action as a public good that players would like the publisher to create. Normally public goods are provided by the government, but we’ve already considered a way the government could help, so let’s look at a more unique option.

Prediction markets are a special type of stock market involving assets that pay out only if a certain event happens. They are usually discussed in the context of their ability to aggregate information about currently unresolved facts. However, Paul Sztorc has proposed that a decentralized prediction market could be used to fund public goods. In our case, the “public good” is an end to whatever we wanted to boycott. To fund it, a special prediction market would be created, and players who wish to help fund the good would buy the state predicting that the good will not be created. If enough funds are raised, the company will choose to purchase a state predicting the creation of the good and discontinue the activity in order to claim the funds.

This strategy also has its share of problems. For one thing, a decentralized prediction market has to exist in order to implement this idea. Even if this condition is met, there’s still the issue of incentives to become a free rider instead of contributing to the funding of the public good. There’s also the question of whether it’s right for players to have to pay extra in order for publishers to listen to them.

There are a multitude of ways in which the weaknesses of boycotts could be overcome. While the ideas presented here are unrefined, I think there may be potential within them. That said, I have no plans to refine them myself, so it’s probable that nothing will ever come of them. However, I will not be surprised if someone eventually comes up with something.

Video game boycotts

2018-01-26T00:00:00+00:00

Recently, many people have been upset by the direction some video games have been taking in regard to certain ideas like loot boxes. One proposed solution is to boycott the offending games. However, there is a fundamental problem with boycotting that makes this very difficult to pull off.

Participating in a boycott is generally not worth it to an individual. A good way to observe this is to use marginal analysis. The marginal cost of participating in a boycott is pretty easy to identify, since it’s simply being unable to purchase and play the game targeted by the boycott. However, identifying the marginal benefit is a bit more complicated.

One way to think of the marginal benefit is to assume that there is a single threshold at which it becomes more profitable for the game developer to give in to the boycott than to continue on with whatever activity is being boycotted. Below this threshold, the revenue lost to the boycotters is less than that gained by continuing the boycotted activity. At and above this threshold, continuing the activity will cost the firm more than it earns them. Thus, the firm will cease the activity if and only if the boycott meets the threshold.

What does this mean for boycotting’s marginal benefit? Well, there’s exactly one person who will bump the number of boycotters up to the threshold. The marginal benefit for this individual is the success of the boycott in changing the company’s behavior. However, for everyone else the marginal benefit of participating in the boycott is nothing. After all, they have no effect on whether or not the company continues the activity. Since the marginal cost is greater than the marginal benefit for at least all but one individual, including everyone who joins the boycott early on (well before the threshold is reached), no one is actually incentivized to participate unless exactly one specific large number of disincentivized people are already participating.

One detail this model fails to account for is uncertainty regarding the location of the threshold. Unless the boycotters can figure out how much the company is profiting from the boycotted activity, they aren’t able to determine which person will reach the threshold. Thus, instead of giving definitive marginal benefits for each person, we can instead model individuals as having a marginal benefit based on the subjective probability that they will reach an unknown threshold.

Let’s say that, without a boycott, a game would be purchased by 10 million people. For the sake of simplicity, we’ll assume that every additional person has an equal chance to reach the threshold. We’ll also assume that there is no chance of reaching the threshold with zero participants, and that all 10 million people participating guarantees that the threshold will be reached. This means that every person increases the probability of a successful boycott by .00001%. Since the expected value of the marginal benefit is equal to the probability of the threshold being reached multiplied by the value of reaching the threshold, we find that a person must value purchasing and playing the game less than .00001% as much as they value the boycott succeeding in order to be incentivized to participate. In other words, unless they want to end the boycotted activity 10 million times as badly as they want to buy and play the game, they will not join the boycott. In fact, that number will always be equal to the number of potential players, so a game that is bought by only 1 million people still requires the players to want the boycott to succeed 1 million times as much as they want to buy and play the game.

Why is it such a big deal that boycotts normally fail? Sure, it’s upsetting that the company won’t stop doing whatever the players hate, but some trade-off has to be made, and getting the game seems to be worth more to them than stopping the company. The problem becomes apparent when you consider what would happen if the players were able to perfectly coordinate as a single group. In this case, the group’s marginal cost and marginal benefit for participating in a boycott are equal to the total cost and total benefit of the boycott. The marginal cost is still being unable to purchase and play the game, but the marginal benefit is now a guaranteed successful boycott. Thus, every player in the group wants the group to boycott the game, assuming the players are willing to wait a short period prior to the boycott’s success to purchase the game in return for actually getting that success.

Why is this result different from when we consider the players acting individually? Because the additional cost for each player joining the boycott is only born by that player while the additional benefit is shared among every player, the fraction of the total benefit the player receives is too small to incentivize them to participate. However, if participating meant they received that sliver of benefit plus a sliver of benefit from every other player, and not participating meant they received no benefit at all, then their marginal benefit is increased to the point where they will participate. Without the players coordinating as a group, the second condition cannot be met thanks to players receiving the benefit from boycotters even if they do not participate themselves.

This situation is an example of what is known as a coordination problem. Without coordination, each player will take an action that makes them better off but leaves everyone else worse off, leading to the group as a whole being worse off as well. However, if the players are able to coordinate, than they can take an action that leaves themselves worse off but makes everyone else better off, leading to all members of the group being better off.

Currently, players are unable to coordinate effectively, leading to situations in which supposed boycotters are actually playing the game they wish for everyone to boycott. This is the optimal strategy for individuals since it allows the players to gain the benefits of continuing to play the game while also giving them some additional benefit from anyone foolish enough to actually do as they say and boycott the game. But from the perspective of the group, it’s a terrible outcome that both causes the boycott to fail and encourages deception.

Not exactly the most effective group

Are there ways to resolve this problem? Possibly, but I don’t think there are any easy solutions. Coordinating large groups is a very complex task, and I’m not sure how much insight I really have regarding this issue. Nonetheless, I will likely propose potential solutions in another post.

This now exists

2018-01-23T00:00:00+00:00

Well, I guess this site exists now. I wonder if it will die before anyone else sees it.