Super-STAR: Dynamically rescaled score runnoff
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I was considering this example from Warren Smith in which range/score gives a true dishonest optimal strategy. The reasoning is because in 2 likely ties an individual benefits from being a tie breaker. 2 liberals, 2 conservatives I vote with maximal strength for the liberal/conservative tie respectively which has 1 approval of my preferred liberal and 1 approval of my preferred conservative regardless of lib/cons preference.
In a STAR system this can be avoided with a {5,4,1,0} vote. For a marginal cost in the score round, using the second best and second worst slot guarantees a maximal vote in the runoff. This does not solve the problem, because now the problem occurs in 3-ways ties. This really rubs me the wrong way because STAR elections which combine a primary and general elections should have many clone candidates with high probabilities of near ties.
My question then is why not extend score-automatic-runoff? The two-round automatic runnoff was originally proposed as a combination of two existing methods I believe. In score-based voting the generalization of a runnoff is a min-max normalization of the remaining range. I was rather surprised that no proposed score voting system seems to use a min-max normalization since this is so applicable to auto-optimizing the dominate strategy. So a 3-canidate runnoff can be a perfectly fair score-based election, with the scores rescaled to reflect new optimal positions in absence of (as reflected by the first round score vote) irrelevant candidates.
3-canidate STAR-style runnoff example:
A voter has elected to use the middle values, this is not often strategically advantageous in plain score voting. If the max/min candidate is eliminated, the voter is no longer using the full range and therefore is not maximizing voting power. If the voter knew their min/max candidate would be eliminated, their second favorite/worst would take the spot. This is the underlying reason why score voting often strategically converges to approval. With this knowledge we can automatically rescale a strategically sub-optimal ballot to optimal.
The generalization of this dynamic min/max normalization means that a score ballot can have an arbitrary number of fair runoff rounds. An honest score vote has the property that score ≈ utility, so the biggest loser of a score election is very likely to be the worst candidate and makes a safe removal as an irrelevant candidate. The remaining votes behave optimally as if that candidate had never run. I don't think you would want to do this system as a full instant-runoff because that might re-introduce some of the same IRV problems. I'm inclined to believe some policy like top 3-5 or top 25% advance to dynamic rescaling runoff.
This method seems to be similar to MARS, serial approval, and Smith//score. I believe this is a strictly better version of repeated approval elections as it encodes the information of repeated approval rounds into a score ballot. Like MARS and Smith//score this method incentives ordinal positioning in a cardinal ballot. I think this Super-STAR method might have some advantages by retaining a score ballot the entire time. Unlike a strict pair-wise comparison the benefits of score's expression and strength of support are maintained the entire time. This method might also need a 0-99 ballot because it incentives using the entire scale. Candidates that would have been tied for 1st can be ranked 99,98,97 with the knowledge that if those 3 make it to runoff you are now automatically strategically voting 99,50,0.
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@kaptain5 Kristofer Munsterhjelm proposed a cardinal Condorcet analogue that looks at three-way combinations of candidates on the EM mailing list.
As an example, in a post a while ago, I considered a Condorcet analog
that might allow for the creation of cloneproof generalizations of STAR,
while still taking intensity of preference into account. Let a cardinal
election restricted to {A, B, C} be constructed by eliminating everbody
but A, B, and C, and then normalizing every voter's ballot to unit lp norm.Then you could do something like: say that A is a "cardinal Condorcet
winner" if, for all X and Y, in the election restricted to {A, X, Y}, A
is the winner. Or A is never a loser.So you look at all three-way combinations of candidates and normalise for those three.
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@toby-pereira Thank you for linking this! It's very interesting that we both had the same idea from a similar reference point. I was most directly inspired by Arrow's 1951 discussion of cardinal utility and why he thought it was silly. In passing he mentions Von Neumann and Morgenstern's cardinal utility and how comparing linear transformation linear transformation gives invalid analysis therefore Arrow focuses on ordinal utility. With a bit of extra context on the differences between optimizing interval utility in voting, and assessing ratio utility of consumer goods; this line of reasoning from Von Neumann and Morgenstern spits out normalized score voting.
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@kaptain5 The ideal would be to find a somewhat-objective normalization with a mechanism like quadratic voting or VCG. Each voter has to "pay for" their rating points by giving something up (like votes they could cast in another election).
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@lime said in Super-STAR: Dynamically rescaled score runnoff:
@kaptain5 The ideal would be to find a somewhat-objective normalization with a mechanism like quadratic voting or VCG. Each voter has to "pay for" their rating points by giving something up (like votes they could cast in another election).
No, because that's exactly the problem with choose-one plurality. I have as a voter the right to support and oppose so many candidates via my vote as I support and oppose in my political stance or judgment. Choose-one plurality single-winner voting says I have to pay a "cost", which is the entirety of my precious vote, as soon as I support one candidate. Support and opposition must be free of cost, because I am a citizen and deserve a full vote, the same as any other citizen.
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@jack-waugh Yes, I meant to reply to this topic earlier. Quadratic voting is terrible as has been discussed elsewhere.
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Top 3 STAR is a known variation.
The thing is that ties in STAR Voting are 10 times less likely to occur than in the current system. Three way ties are an extreme edge case. The scenario where the 3rd place score getter could beat the finalists in the runoff is also an extreme edge case and not one that is predictable enough to influence voter behavior or strategy. (There's also the argument that that candidate doesn't deserve to win.) So, imo, this is a non-issue in elections at scale.
I assume this post is just for fun, because the puzzle is interesting. There is always a way to approach perfection if complexity is not an issue and comes at no cost, but complexity is a huge cost and barrier to implementation and adoption.
In elections that are not to scale (a vote by a board of judges for best movie, for example) ties are easily solved by super simple options like a runoff between the tied candidates or any number of other mechanisms that wouldn't make sense for a real scaled political election.
For elections at scale here's our official tie-breaker recommendation: starvoting.org/ties
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@jack-waugh said in Super-STAR: Dynamically rescaled score runnoff:
@lime said in Super-STAR: Dynamically rescaled score runnoff:
@kaptain5 The ideal would be to find a somewhat-objective normalization with a mechanism like quadratic voting or VCG. Each voter has to "pay for" their rating points by giving something up (like votes they could cast in another election).
No, because that's exactly the problem with choose-one plurality. I have as a voter the right to support and oppose so many candidates via my vote as I support and oppose in my political stance or judgment. Choose-one plurality single-winner voting says I have to pay a "cost", which is the entirety of my precious vote, as soon as I support one candidate. Support and opposition must be free of cost, because I am a citizen and deserve a full vote, the same as any other citizen.
I think the thread you linked is based on a misunderstanding. The quadratic voting penalty is applied across different races, not in the same one. So, for example, you can either cast 10 votes for President, or you could cast 5 for President, 5 for Governor, 5 in some ballot initiative, and 5 in Congress. (Adds to 100.)
The squared-cost penalty is chosen so you'll honestly reveal your relative preferences across different issues, under an impartial culture model. I assume you could do better than an impartial culture model, but the point is more that you should be able to trade influence across decisions to have a bigger impact on the issues where your preferences are stronger.
