VSE for PR?
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Warren Smith's concept of Bayesian Regret (adapted into VSE) led to an objective method of analysis for single winner elections which allows researchers to overcome biases and competing metrics of "fairness".
In the 20+ years since that idea no one seems to have adapted Bay Regret/VSE for multiple winners. Proportional systems are typically assessed with a few different methods which boil down to different ways to assess error compared to the popular vote. This is not necessarily the same thing as finding the set of multiple winners which maximizes utility.
I doubt there has been a lack of effort since a fair comparison would let STAR fans assert superiority over even more voting methods. So what is the hold up for assessing utility of PR elections?
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The issue is that defining VSE for the multi-winner case is, uhh, complicated. In particular, PR doesn't do a good job of satisfying VSE under the most intuitive model, one where voters' utilities are additive, i.e. satisfaction equals the sum of scores you assign to each candidate. If that was actually the case, the best methods would be winner-take-all (pick the candidates with the highest scores).
The ideal situation would be to have voters score each set of candidates, e.g. "a committee with A, B, C has a score of 3; one with A, B, D has a score of 5, ...". Then we could maximize the sum of scores. However, that's completely impractical for voters, it's difficult to model utilities, and a method like this would be extremely vulnerable to strategic exaggeration.
So, in the proportional context, so far we've found it easier to just deal with pass/fail criteria rather than VSE. That's not to say VSE couldn't be extended to the multiwinner context, it's just that it's complicated and we don't know how yet.
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@lime I think that since multiwinner elections are generally for electing legislatures, we can say that generally the goal is for the set of winners to be able to vote on laws in such a way that the laws passed maximize voter utility (i.e. come closest to their preferences on the issues). Now since this is difficult to simulate, how about simplifying it down to an election-based process: have the winners of the multiwinner election conduct a single-winner election among themselves to choose a leader (presumably using whatever single-winner voting method the original multiwinner election's voting method simplifies to), and then see how much utility the original voters in the multiwinner election receive from that leader compared to the amount of utility those original voters would get from the leader they would have elected if they had themselves voted in the single-winner election.
Essentially, test how much utility voters would get from the Prime Minister chosen by Parliament versus their utility if they directly elected a President instead.The same idea is covered at [https://rangevoting.org/BRmulti.html](link url)