Technically Exists

The motivation behind SPSV, part 5

2020-10-27

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.

Read more

The motivation behind SPSV, part 4

2020-10-26

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.

Read more

The motivation behind SPSV, part 3

2020-10-25

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.

Read more

The motivation behind SPSV, part 2

2020-10-24

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.

Read more

The motivation behind SPSV, part 1

2020-10-23

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.

Read more