Over in the “hit-piece” discussion that has unfortunately become necessary, RobBrown says

With STAR, you just give Nader 5, Gore 4, and Bush zero.

This ignores the Gibbard Theorem, which says that no voting system relieves you of taking into account your estimate of where other voters stand, if you want to bring to bear all your power.

Sara_Wolf says

With Score the best strategy is generally to give all your candidates

min or max scores, while also being sure to max-score your lesser-evil

if you don’t think your favorite can win.

No, I’m pretty sure this is not the best strategy. It is to give your best candidate the top score, your compromise candidate .99 of the way between the minimum and maximum scores if you think your favorite would only get .01 proportion of the votes in choose-one plurality, and the other candidates the minimum. This strategy will cause support for your favorite to be reported, while providing substantial opposition to the worst candidates (as you judge them). If sufficient proportion of the electorate agree with your stances toward the candidate and they follow this same strategy, your candidate will win. But if you vote Approval-style, your candidate will tie the compromise candidate.

I want to end by stating that Score Voting is a great voting system.

That it’s a lot better than Approval, . . .

I contend that all Range Voting is equivalent, regardless of whether it is Approval or finer grained. My grounds are that over the long term, voters figure out pretty good strategies, because Darwin, and because we can see that with the English system (choose-one plurality) (FPtP), the Americans have figured out the main strategy for it, which is to discourage moral candidates from running, on grounds that they will split the vote with the lesser evil, resulting in the election of the greater evil. And my second ground is that if the range is too coarse, the voters can consult a random (or pseudorandom) number and approve the candidate in question with a probability that reflects the score they would like to give.

Wolk and respondents mention a contention that Range Voting provides incentives that some regard as a deal-breaker. I don’t understand this contention. So far as I have heard, the only incentive Range provides is to exaggerate support for a candidate between that for other candidates but never crossing one candidate over another. Is there an argument running around that says it gives an incentive to cross them one over another?

Of course I think the Venn diagram errs where it separates Approval from finer-grained Range (i. e. Score). I argued above that they are equivalent once the voters figure out strategy, and I argued that the voters eventually will figure out strategy.

I don’t see why Accurate is a distinct concept from Equal. It seems to me that “winners accurately reflect the will of the people” exactly when the people have equal power to one another in determining the winner.

Honest is nonsense given the Gibbard theorem.

RobBrown says

the gold standard of “fairness” is whether it selects the “first choice of

the median voter”.

Any kind of first-choiceism raises my suspicions because it smacks of IRV.

Who is the “median voter” under an “Everybody-Loves-Raymond” scenario? For example there are two voting factions and three candidates and faction F0 consists of 51% of the voters and their true scores are A 1, R .99, B 0 and the position of the remaining faction is A 0, R .99, and B 1. Who is the median voter, and why should she have her first choice when clearly R gives much higher VSE than A?

OK, reading down, I see that for evaluating Acccuracy, starvoting.us broadens the criteria beyond mere equality, including in particular the Condorcet criterion or constraint and VSE simulations. The trouble with VSE (or Baysian Regret to look at basically the same concept from the other side) is that they start with an assumption about what strategy the voters will use. I don’t whether in each case this assumption is good. And as for Condorcet, it relies on ranking and throws away strength of preference within a ranking.

I want to suggest that STAR and Approval are equivalent. Since both of them pass the Frohnmayer balance test, and since neither of them makes a voter’s valuation of one candidate depend on the voter’s valuation of another candidate, they give equal power to the voters, one voter to another. If a given electorate faced with a given field of candidates would elect different candidates with STAR and Approval, we would have to conclude that at least one of the outcomes would disadvantage one voter unfairly and give another voter an unfair advantage, because that system did not produce the same outcome as the other system, which other system is fair based on its according equal power to the voters, one to another, based on its passing the balance constraint and allowing independent valuations of the candidates. However, the same consideration applies to the first system, and so they can’t produce different outcomes. Therefore, they are equivalent.

Participants keep writing as though there were a background assumption that for Approval, a threshold-based strategy is what people will use or what would work best for them. I don’t think this is the case. The best strategy is to decide how you would vote in fine-grained Range and simulate this using probability when you decide whether to approve.