Considerations for Proportional Representation

[SaraWolk]

Today I re-read the write up for Andy Dienes's Proposal for Threshold of Equal Shares, which is a cool proposal. This thread isn't for discussion on that method, but rather to share some thoughts on the considerations that motivated the proposal in the first place, described in the "Motivation" section of the Electowiki page.

As a disclaimer, I just want to be clear that my comments are not an argument for or against TEA or for or against other types of 5 star PR methods. Take what I say below at face value and don't try and assume its an argument for or against any systems.

Andy writes:

Many designs for sequential cardinal proportional methods rely heavily on the assumption of linearly additive utilities over sets; that is, if a voter's score for candidate A is 3, and their score for candidate B is 2, and their score for candidate C is 5, then the voter is presumed to be just as happy with the outcome {A, B} as they would be with {C}. The problem with this line of thinking is that the number of seats in a committee is fixed, and each candidate elected comes at the opportunity cost of a more-preferred candidate. It may not even be possible to map a voter's preferences over sets of candidates to a single linearly additive utility for each candidate individually.

I absolutely agree that for a given voter the election of their 5 star candidate isn't equivalent to the election of their 3 and 2 star candidates.

That said, I don't think that's the question on the table. For example, let's take a three winner election where our voter is scoring honestly. Candidate A is their 5 star favorite, B is 4 stars, C is three stars, and so on down to F is 0. Candidate G is also 0.

In this case, I do think it's reasonable to assume that an abstract voter's utility is equally represented if they get their three winners were scored 5, 0, and 0, compared to if they had elected winners they'd scored 3, 2, and 0. At least on average.

The key here is to remember that the end goal of elections is to elect a governing body that will produce representative legislation. The goal is not just to have representation on the governing body. For our voter under the first set of winners their representative will likely be outvoted on every issue that comes up. The result is a government that passes legislation they actually hate.

In contrast, under the second set of winners they may not have anybody advocating for their exact positions, but they will have two people who can advocate for a more moderate version of their positions and who can prevent the other side from passing morally bankrupt legislation.

He continues:

Another drawback of the linearly additive utility assumption for set-valued preferences is that it creates an inherent trade-off between a voter's ability to express preference within their own coalition, and their ability to express preferences over other coalition's candidates. If a quota' is measured in score, in that five quotas of 3 stars is equivalent to 3 quotas of 5 stars, then coalitions are rewarded for being more cohesive,' in the sense that they can only guarantee their deserved number of seats if every single member of the coalition awards the maximum score of 5 stars to every single candidate in that coalition. Any amount of vote-splitting or intra-party preference will lead to lower sums-of-score, and will be regarded by the method as a lack of cohesion and punished with fewer seats.

This is a very good point. That said, I can see an obvious solution. Party Primaries! (I'm not generally a fan of primaries when the number of candidates is under 5, or when the election is single-winner, or when there is only one competitive party, but PR elections will likely be none of the above.)

Multi-winner elections by nature already increase the number of candidates competing in one pool, so this already adds to the need for a primary to help narrow down the pool of candidates to a set that voters can reasonably research.

For a PR election it makes a ton of sense to me to have voters vote in a primary for their party or coalition of parties (for parties that want to formally coalition). Voters who are unaffiliated can pick the primary of their choice to vote in. This would determine the party or coalition list. Then in the general election, voters would know the list for each party and would be able to vote between the parties/coalitions.

Takeaways:

• In a multi-winner election you can't look at a voters utility without considering the full winner set. A voters utility improves if candidates they like more win, but also if candidates they like less lose.
• In a multi-winner election real utility is not determined by the election of candidates a voter likes, but in the efficacy of that body to do beneficial work for that voter. In evaluating voting systems we have no empirical way to know what the legislation produced will be, but we have to remember that better outcomes are still the end goal, not token representation.
• The main factor that determines if a proposal is passed or blocked by a legislative body is if they have a majority of yes/no votes. Thus a voter is better served by having a majority, even if that majority is less in their corner. At least that way they can make progress towards a larger goal rather than be ineffective, or worse, lose ground.
• The exact voting method algorithm itself is only one consideration and variable. Frankly, the type of PR algorithm may make a lot less difference than things like districts, thresholds, ballot style, number of candidates, ballot access rules, and whether the election is partisan or non-partisan.

Even if you agree with everything I just said, none of these points are points against TEA. There are other arguments for and against prioritizing voters top choices (but introducing bias) and for and against safeguarding against strategic voting (but introducing complexity). These arguments still stand and can be considered with other pros and cons not mentioned here that are also worth taking into account. IMO proportional representation is all about the details and zooming out is as important as zooming in.

[Jack Waugh]

I judge all your points above valid, relevant, and well explained. I also appreciate your caveats about there being other considerations as well, etc.

I think these points argue for Liquid Democracy.

[Toby Pereira]

Interestingly, the KP Transformation, which is a way of converting approval methods to score methods, does not work on the basis that you can simply add up a voter's score for each elected candidate to see how satisfied they are. If scores are out of e.g. 5, then each voter essentially has 5 utility slots and the top one will only be satisfied by a score of 5. So two candidates with scores of 2 and 3 being elected will mean that 40% of the voter's utility slots will be untouched. A 0 and a 5 mean that all slots will be satisfied to some extent but none more than once.

I think the KP transformation is generally good because it gives maintains good criterion compliance when added to an approval method without adding nasty surprises. And it's simple. Essentially all of the debate between Allocated Score, Method of Equal Shares, TEA etc., are about what to do with these messy scores that are hard to deal with when you use a score method rather than an approval method. KP sorts that out simply with generally better criterion compliance. So the consideration of TEA versus those other methods then becomes irrelevant.

And as I mentioned in this thread, all the subtractive quota methods are really just weak approximations of Phragmén-based methods. So I'd use Phragmén + KP as the basic starting point of a method you have to do better than. If determinism isn't essential, you can do better still.