Best posts made by Marcus Ogren

I'm worried about the strategic implications of this. In the single-winner case this is Majority Approval Voting (assuming you're using the Droop quota), and even with more winners this has all of those strategic issues.

• Suppose you are part of a faction that comprises ~1.2 quotas and has fielded two candidates, one of whom you like more than the other (you hate every candidate outside of your faction). Your faction is very likely to win one seat, but it won't win two. Here you want to have your ballot count only as an approval for your favorite as far into the tabulation as possible, so you shouldn't give your second choice a score greater than 1. Even bullet voting is reasonable; if the vast majority of voters in your faction are giving their second choice a 1, bullet voting is the only way to make your ballot count in the decisive round. (This is, of course, the chicken dilemma.)
• Suppose there's a two-party system. The other party has both moderates you tolerate and extremists you hate, and you'd rather they elect more moderates than extremists. Still, the main thing you want is for your party to win more seats than them. Here, giving even a 1 to a moderate candidate in the opposing party is a big mistake. It won't make a difference at all until all scores of 1+ are counted as approvals, and at that point you still want to favor your party's candidate over the opposing moderates.

These are simplified examples, but the simplicity is not necessary for such problems to manifest. I'm not claiming that it's never strategically optimal to give a candidate a 4, but it's pretty atypical. It's strategically optimal to use lower scores than other voters do, such that they're supporting both their own favorite(s) and your favorite(s) while you're only supporting your favorite(s). The only equilibrium involves 5s for a voter's favorite(s) and low scores for everyone else.

Under Threshold MES, voters who ignore strategy lose a lot of influence, and when voters are strategic the expressive power of the 5-star ballot is mostly wasted. I am pessimistic about it reducing political polarization any more than any other PR method would; I actually expect it to be worse than STV in this regard since parties would be heavily incentivized to get their voters to not give candidates from any other party a score greater than 0 and this would encourage divisive attacks. Similarly, candidates would be incentivized to play exclusively to a party's base (and perhaps to some "sucker" voters in other parties who vote as would make sense in single-winner STAR).

@andy-dienes said in Threshold MES:

I do really want to emphasize that one of my main theses for this design is that the mere existence of 'sincere' utilities for each candidate, when in a proportional multiwinner context, feels somewhat nonsense to me.

In principle, I fully agree with you. In practice, I think assigning utilities to each individual candidate works pretty well. An individual voter will only have a marginal effect on the outcome; questions that cause the individual-candidate-utilities model to break down (such as comparing between electing 5 candidates you love, 3 candidates you love and 2 candidates you hate, and 2 candidates you love and 3 you hate to a five-person committee) become irrelevant (at least usually). If a single ballot can cause at most one of the winners to be different, I can't think of an example off the top of my head where the model of having individual utilities of each candidate and maximizing the sum over all the winners breaks down.

Let's say the percentages of the electorate are respectively w, x, y, z%. This is (kind of) an instance of laminar vote splitting---at least if there is some candidate popular among the entire Left wing, and likewise for the Right. To me, I would prioritize the guarantees in this order

• Left gets at least (w+x)% seats and Right gets at least (y+z)% seats

• Within Left seats, the Far and Center factions get seats in a ratio w:x, within Right seats, the Far and Center factions get seats in a ratio z:y

• Residual preferences respected (i.e. cross-party preferences and low scores come into play to flip small win margins or change election order within party)

I have two major points of disagreement. First, I place no intrinsic value whatsoever on having guarantees; all I care about are results and incentives. I am completely indifferent between having a result occur with it being guaranteed to occur and it occurring without a guarantee. Second, I consider the second point to be undesirable. In my example, voters have somewhat stronger preferences for who wins within the opposing party than within their party, and I don't think the weaker preferences should take precedence over the stronger preferences. Also, points 2 and 3 are in direct conflict, and I care about point 3 because it encourages depolarization.

The proportionality guarantees mean that no matter how much strategic jankery happens, as long as Far Left voters give Far Left cands higher scores than Center Left cands and vice versa, and all Left voters give Left cands higher scores than Right cands (and again, vice versa), then both 1. and 2. have to hold.

The stringent conditions (e.g. "all Left voters") make these guarantees seem weak to the point of irrelevance; "strategic jankery" that is well-justified and outside your allowed parameters will void these guarantees entirely. And strictly speaking, I don't think these guarantees are strong enough to prove what you want. Like, if most Left voters give the Left candidates a score of 3 and Right candidate a score of 0, but slightly less than a full quota of Left voters give the Left candidates a score of 5 and the Right candidates a score of 4, these latter Left voters will function like Right voters who will fill the quotas of Right candidates. Contrived, I know, but still. you need to assume a lot, including some pretty unreasonable things, in order to get a mathematical guarantee.

Conversely, in Allocated Score (with or without runoffs), we can only get guarantees 1. and 2. if every Left voter min-maxes their candidates. And in fact if they start peppering 2s to the opposing party I think it's quite likely that they will lose seats.

True with respect to guarantees (though I don't care about guarantees). As for the latter point, more precisely they can lose seat. Most of the seats will be decided by the filling of quotas; so long as their voters don't fill the quotas of opposing candidates, giving 2s to the opposing party is only harmful for winning the final seat. Still a solid argument against giving out these 2s, but I don't think it's an overwhelming one.

I think our big disagreements are (1) Should a voting method favor moderates over extremists? and (2) Are formal guarantees valuable? Our disagreements seem to be more over what a voting method should do than over what certain voting methods will do. I am not particularly optimistic about coming to an agreement on these points, but I think the agreements we have reached are valuable.