Yee animated graphical, Does Score favor centrist candidates?

Does Score voting augment centrist candidates? At 4:09 Mark F says: “In Score, candidates benefit by being in between the other candidates.” and “Score voting has a center expansion”
So, in theory, if you believed in Centrism you’d prefer Score/Range voting?

  1. It doesn’t favor “centrist” candidates; it favors “candidates who are similar to a crowd of other candidates”. So if there are a bunch of similar extremists running against a moderate, the extremists get an unfair advantage.
  2. This effect is due to voters “normalizing” their ballots. If your true ratings are 2, 3, 4 for instance, you would exaggerate to 0, 3, 5. With even more strategy, you would max out multiple candidates at the extremes, and this effect would (I think) be even worse.

As WDS says:

We begin (lefthand picture below) with honest (but “rescaled” – each voter rescales utilities so her best choice is 99 and her worst is 0 before voting them) range voting. The picture is very similar to the Voronoi diagram, but slightly distorted; and note that the magenta candidate is outside its win-region. [If there were no rescaling, or if there were an additional candidate very far away (well outside the pictured area) then the distortion would have been zero and range voting would have yielded exactly the Voronoi diagram.]

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Isn’t 2, 3, 4 as likely to be normalized to 0, 2, 5? What remains of the alleged bias after you account for that? Is it safe to assume, then, that Score’s apparent bias is a result of the simulators following the nursery school custom of rounding up half-integers?

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I don’t think that matters; I think it’s the 0s and 5s that cause the effect.

I don’t think rounding matters, either, and the same thing would happen with [0, 1] real number scores, but I could be mistaken. The rounding code is here:

Also I think this effect is roughly the same thing that happens under Borda count (which is also points-based and normalized, in a sense), which makes it advantageous to run many similar candidates:

Borda center expansion is shown here:

With Borda voting, the result is the opposite: the presence of the red candidate is actually helpful to the green candidate, expanding the green winning region slightly.

I’m a bit new, “normalizing” refers to finding medians and marginal medians within the range. Each voter would do that individually. But I would imagine, for example in a very rural midwestern town the medians will tend to be toward the right extreme and in a progressive urban city the medians would tend toward the left. The centrist dilema arises when public sentiment is different than what a jurisdiction experienced as candidates in the past. A population might say the want free widgets and when a candidate presents themselves to give them that, voters chose a more centrist candidate that won’t give them that. Because people have a cynical belief that real change isn’t possible, so they tend to move toward a center that aligns with history, instead of towards the extreme that would give them the change they want.

If you get what I’m saying, is there a mathematical interpretation, an index, or some measure of that? Perhaps, the Overton Window?

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How so?

Sorry, could you explain? It appears to use .2 and .6 as the thresholds for Score 1-3, whereas a rational voter would use 1/3 and 2/3. Using .2 makes it less likely for an intermediate candidate to be minned, and using .6 makes it more likely for him to be maxed, so how would that not help intermediate candidates?

Association fallacy. Borda’s vulnerability to teaming is due to the effect ordinally intermediate candidates have on the score differences between candidates on either side of them in Borda. But in Score, normalization is based entirely on the favorite and least favorite; you could add a billion intermediate candidates, and it wouldn’t affect the scores of the other candidates. Even in min-maxing, where they would have an effect, it wouldn’t advantage them or other intermediate candidates.

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You seem to be saying that Score does favor intermediate candidates. My second question, has more to do with a human phenomenon, a tendency that I and others, seem to be observing and not having as much to do with voting methods.

No, I’m saying Score doesn’t favor intermediate candidates. If indeed the thresholds used in the simulation of Score voting behavior are .2 and .6 (they may not be; it’s quite possible I’m reading the code wrong, so let me know if I’m in error), that would explain the illusion of bias. .2 and .6 give an advantage to intermediate candidates; the rational thresholds, 1/3 and 2/3, do not.

I’m definitely sympathetic to that point of view. I’m not aware of any actually-existing voting method that’s center-biased (though theoretically the dual of any extreme-biased method is center-biased). But in terms of human center-bias, yeah, I think there’s both a benign version of that, which I discuss here, and a positive feedback loop, where, like you said, a thing is regarded as extreme today, and consequently marginalized, because it was extreme yesterday. But I don’t think that’s well-simulated by lowering score thresholds in the simulations.

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How do election scientists compensate for the Overton Window?

It depends on whether you mean compensate by reforming the voter model or compensate by reforming the voting system, and on the precise definition of the Overton Window.

Does the Overton Window split candidates into two sets, S and T, each member of S having perceived win probability 1/|S| and each member of T having perceived win probability 0? That would hurt T in most systems, either help or hurt it in Modified Borda and non-ISDA Condorcet methods, and help it in methods where you vote against candidates. In Anti-plurality, T’s members would tie each other for first. In Coombs’ method, S would only have a chance if it included a majority winner; otherwise, the winner would necessarily be whoever would have won in the absence of S.

But I think what you have in mind would be better modeled by moving any candidate outside the Window to the closest point on the edge of the Window. That would have the effect you described, supporters of an extreme idea being less supportive of candidates with those ideas. It would also have the opposite effect on opponents of the idea. For example, I think Bernie Sanders would have had a decent shot of beating Trump despite the number of Biden supporters opposing socialism being greater than Biden’s margin of victory. The Window has a lot to do with that: anti-socialist anti-Trumpers would have expected Congress or the Supreme Court to block socialism anyway.

Finally, the Window could be defined such that the utility of a candidate outside it is equal to the voter’s disagreement point, i.e. the utility of the results of the election being rejected (as in a coup or revolt). That wouldn’t work for spatial models, though, because they (unwisely, I think) use ideal points instead of disagreement points.

Another explanation for the illusion that Score favors centrists can be found here. Using Yee graphs, Approval with a random or stable threshold was found to be unbiased, but Score with normalized scores and (to a much greater extent) Approval with an unweighted-average-candidate (UAC) threshold were found to be pro-centrist. Elsewhere, “Bullety Approval” (bullet voting with probability p>0 and UAC with probability 1-p) was found to be smarter even in the zero-information scenario, suggesting that setting the approval threshold to the p<1 power mean utility loss would also be smarter; and there’s obviously some value of p (in either approach) for which Approval voting is unbiased.

So if Approval’s bias is dependent on a particular (foolish) strategy, why wouldn’t Score’s be? Even if we confined Score voters to be “strongly sincere” (i.e. use a linear scale) instead of wise, why would we expect them to use their favorite and least favorite as its min and max (indeed, don’t we find failure to use max and min everywhere we find honesty?)? A common scale (from the length of the space to 0, or at least from one’s least favorite’s distance to 0) would obviously be more sincere, so it appears Score is only biased when voters are irrationally sincere but not too sincere.

Just as Choose One voting (and IRV) favors candidates who are more polarizing or more specifically those who run one candidate who stands out as opposed to a few similar candidates, score voting has a bias in the opposite direction.

Score and Approval voting favor the candidate in the middle of the electorate’s political spectrum as they will likely get support from both sides, and because of the strategic incentives, they favor those who are seen as most electable. You should always give your preferred front-runner a max score in Score, and always approve your lesser evil front-runner in Approval.

With STAR Voting there isn’t a need to give your preferred front-runner/lesser evil a top score. As long as you show a preference between the finalists, the runoff will do that for you… if it comes down to that.

One thing I’ve been realizing is that many people who are versed in voting theory may prefer IRV or Score/Approval because of these biases.

A number of Green party people see an anti-centrist bias as helping them, though the advantage for far left or right parties is canceled out by the IRV glass ceiling; The fact that voters who prefer a strong underdog are the most likely to have their favorite eliminated and their 2nd choice not counted anyways.

On the other side many die hard Score/Approval fans who prefer it to STAR seem to identify as centrists and see a centrist bias as a good thing. For those thinking that way I’d caution that who is seen as “electable” is strongly influenced by who has raised the most money, who is the incumbent, who has the institutional support of the status quo power brokers and mainstream media. Bias is not good, even when we see it as working in our favor.

For me my goal is for the voting method to not put a finger on the scales either way. A consensus candidate with broad support could fall anywhere on the political spectrum, which I don’t think is as linear or even 2 dimensional as we often imagine it.

That’s a misconception. You should only max candidates with positive prospective rating, and it’s possible for both frontrunners to have non-positive or even negative prospective rating. Indeed, the phrase “lesser evil” implies negative prospective rating, just as “lesser good” (of a frontrunner who is still good, the probability of a worse underdog winning being sufficiently high, just not as good as the other frontrunner) would imply positive. What rational person would regard a candidate as “evil” just because he’s not their favorite candidate?

Granted, given certain assumptions, it’s more likely to be rational to max at least one frontrunner than it is to be rational to max at least one of a random pair of candidates, but given those assumptions it’s also more likely to be rational to min at least one frontrunner than to min at least one of a random pair of candidates. How is that an advantage?

What if it comes down who makes the runoff? What if your failure to max the best frontrunner causes the worst frontrunner to face an easier opponent? Or a worse opponent? Don’t get me wrong, a strategic STAR voter would sometimes separate (by one point, sometimes dishonestly, i.e. when there’s closer to 0 points’ worth of preference) candidates a strategic Score voter would give the same score to, but once again you’re ignoring the other side: a strategic STAR voter also sometimes gives the worst frontrunner a higher score than a strategic Score voter would. Again, where’s pro-centrist or pro-frontrunner bias?

In the STAR runoff every vote is an equal fully powerful vote, regardless of the scores given. The runoff measures the number of voters who prefer each finalist. One ballot = One vote. If I gave the finalist A 0 stars, and finalist B 2 stars, then my full vote would go to finalist B. The runoff normalizes the ballots so that can’t happen.

I was referring to your failure to max B preventing B from making it to the runoff in the first place.