Interesting argument against STAR and for Score and Approval

It’s possible, in both STAR and Score, to get a utilitarian winner. In Score, vote honestly, and in STAR, vote somewhat strategically to ensure two utilitarians make the runoff, so that one of them is guaranteed to win. However, there is an argument that if the minority votes strategically in STAR to ensure two utilitarians make the runoff, the majority may feel shortchanged simply because of the use of strategy, and attempt to counter with strategy by zeroing out the utilitarian candidates; if the minority vote honestly, it’s unlikely that two utilitarians make it, because they both lose points due to voters trying to differentiate between them for the runoff step, and thus the majority can always take the second spot in the runoff and win. In other words, the majority might be okay if the utilitarian candidate won under honest voting, but wouldn’t be okay if they won under strategic voting, even if the utilitarian candidate was pretty high-utility for them overall; and further, because of this, only Score can really hope to elect utilitarian winners compared to STAR. How likely might this be?

  1. This can backfire; how does this “majority” actually know it is a majority? They could elect the “minority” candidate by mistake.
  2. In systems like Score and STAR, it would be nearly impossible for all voters of a given ideology to bullet vote like this. (E.g. some may be skeptical of point 1; others may not actually like the “majoritarian” as much as the compromise, because there are some voters who really are in the middle).
  3. Does this not work equally under Score? I fail to see how having two winners makes any difference. In both systems, a majority conspiracy can just vote their fave max and all others min, and the fave wins.
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They might live in a district that is heavily liberal or conservative.

With STAR, the majority can give the compromise a 1/5 to protect themselves if they themselves don’t make the runoff.

It works the same in Score, but the argument is that the majority will think "We’ll tolerate losing utility, but only if everyone is voting honestly i.e. playing the game ‘fairly’. If anyone tries to play ‘unfairly’, we’ll use strategy to get more utility for ourselves as well i.e. preventing compromise and ensuring the minority gets 0 utility.

Even then, how can that many voters conspire to do something of that magnitude? If there is a 60% majority but even a third of those voters do not follow the strategy, a compromise candidate can win.

The honest utility of compromise candidate: 60 x 3 + 40 x 3.5 = 320
The score for the compromise candidate: 40 x 1 + 20 x 3 + 40 x 5 = 280
The score for the majority candidate 60 x 5 = 300
So the majority makes the runoff and beats the compromise.

It’s not only a question of 20 overall utility lost, but making sure the minority has some utility; they get 0 with the majority candidate and 3.5 with the compromise. That’s where STAR may or may not falter.

I don’t understand your definition of “utilitarian winner”. Why would a minority vote strategically for a utilitarian winner?

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The argument is essentially that if only one utilitarian candidate makes the runoff, they lose to the majority preference, so two utilitarian candidates must make it for one of them to win, but the two utilitarian candidates both lose points because voters may have a slight preference between the two that they express by lowering one candidate one point below the other, which on net reduces each’s scores. The only way, in this scenario, to make sure both utilitarians make the runoff is for the minority to score them both higher strategically, but this might incense the majority who then zero out the compromise candidates because they don’t want to lose utility. You can find worked examples at https://www.reddit.com/r/EndFPTP/comments/cvsoet/comment/ey9v4zo

How would the utilitarian candidate not also get the majority preference in the runoff?

With a 60% majority giving their favorite a 5/5 and the compromise a 3/5, and the 40% minority giving the compromise a 3.5/5 (on average), the majority-preferred candidate has 300 points and the compromise has 320 points.