Making Voters Equal in Power
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@jack-waugh said in Making Voters Equal in Power:
(regarding score voting and the temperature voting thing)I say that since it limits the pull of a single voter to a range that could be normalized to between 0 and 1 or if you will between -1 and 0 or between -1 and 1, whatever is convenient to compute or argue with, that prevents anyone from having more pull than anyone else, provided that everyone uses the optimal tactic for the faction to which they belong.
Score voting is almost like saying "everyone write down their preferred temperature for the office, but it has to be between 65 and 75 degrees. Then we'll pick the average."
Sure, there is a limit to how much they can exaggerate, but the smartest voter is going to try to guess what others will pick, and then exaggerate their preference as far as they are allowed.
@jack-waugh said in Making Voters Equal in Power:
I had to admit that my absolutist thinking about it had been too narrow and left out valid considerations.
Cool.
And keep in mind, even if we say some issues are lacking a middle ground, you can still have a middle ground candidate. Example: Liz Cheney. She is far to the right/Republican side on some things, and far to the left/Democrat side on the "DT must not be re-elected" issue. That sort of averages out to middle ground.
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@rob said in Making Voters Equal in Power:
Score voting is almost like saying "everyone write down their preferred temperature for the office, but it has to be between 65 and 75 degrees. Then we'll pick the average."
Room temperature is on an interval scale. If you take the median, you are treating it as an ordinal scale. I doubt whether candidates are on either an interval scale or an ordinal scale. The numbers that Score voters put on their ballots are not proposed temperatures or anything like that. They are related to the voter's affinity toward each candidate. The equivalent for office temperature would not be my submitting a single number. It would be my submitting a score for 65F, a score for 65.1F, a score for 65.2F, and so one, up through a score for 75.0F.
I don't remember how the discussion went that convinced me that Score is preferable to Majority Judgment or Bucklin. I think those are the outcome of the medianist thinking.
Sure, there is a limit to how much they can exaggerate, but the smartest voter is going to try to guess what others will pick, and then exaggerate their preference as far as they are allowed.
If I remember correctly, Warren D. Smith said that Score never provided an incentive to invert ranks. If that is correct and he was correct, that means that "so far as they are allowed" may be too far for what would serve their interests.
Note by contrast that RCV IRV Hare without equal ranking does provide an incentive to invert ranks (an implication from Gibbard and the fact that the ballot is nothing but a total order).
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Making Voters Equal in Power:
Room temperature is on an interval scale. If you take the median, you are treating it as an ordinal scale. I
It is not a perfect analogy, you are looking at it too literally to see the point I am trying to make.
The point is that score gives you an incentive to exaggerate, but puts an artificial cap on it. As opposed to all voters voting sincerely being a Nash equilibrium, an idea expressed by my temperature/median thing (with near perfection). With discrete candidates, Condorcet methods comes far closer to this ideal, but there is a lot of messiness (due to there being discrete candidates) which can obscure things..
Anyway, all voters voting sincerely under score is not a Nash equilibrium.
Using average with the temperature voting is the extreme, where the incentive to exaggerate would make it insane.
But yeah, I think you'd do better to try to see what analogies are trying to demonstrate, rather than trying to pick apart where they differ.
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@rob said in Making Voters Equal in Power:
As opposed to all candidates voting sincerely being a Nash equilibrium
I assume you meant to say voters. And is this possible? Is there a system that does this? By the Gibbard theorem, there is a better way to vote than "sincerely". This is of course an existence theorem; it does not construct the way. So maybe with some systems, even though the way exists, it's too hard to find for practical purposes, even for monied factions. I don't know.
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Anyway, all voters voting sincerely under score is not a Nash equilibrium.
Blimey, of course not! But what about all voters voting strategically under Score?
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Making Voters Equal in Power:
And is this possible? Is there a system that does this?
I believe Condorcet systems are very, very close to this. They are not perfect, but nothing is. (again, at risk of tiring people with this, I think my temperature example is a good model for a system where honest voting is a Nash equilibrium. So is majority for a two-way race, but I don't like that example as much because two way races are inherently divisive and there is obviously no middle ground)
But what about all voters voting strategically under Score?
Well, think about that. In a sense, it a Nash equilibrium by definition. Nash equilibrium is another way of saying that everyone is being maximally strategic. The ideal is where sincere voting and strategic voting are equivalent.
You can't vote strategically under Score (or approval, or choose-one) until you know how others vote. The only way for it to actually reach that equilibrium is in a context where everybody gets to adjust their vote after seeing how others have voted, until it stabilizes.
So that isn't a desirable equilibrium, for several reasons. One, you can't vote "strategically" without a more cognitive effort and research. Two, many people find that voting insincerely is against the spirit of the method, so they won't do it.
So now you've got a method that disadvantages people who are some combination of a) bad guessers, b) bad at math, or c) have a strong sense of ethics and honesty. That doesn't seem to be "equal."
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@rob said in Making Voters Equal in Power:
You can't vote strategically under Score (or approval, or choose-one) until you know how others vote.
Do you have to know how they will vote, or does it suffice to know their affinities toward the candidacies?
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Making Voters Equal in Power:
Do you have to know how they will vote
Really you have to know how they will vote. I have referred to this as the "hall of mirrors" effect.
Perot, Clinton, Bush was a good example of this. Going back to Nash equilibrium, I think there were multiple equilibriums in that election (under choose-one), one with Clinton winning, and one with Perot winning. A lot of people liked Perot best but weren't confident enough that similar people would vote for him.
This would be true for Score as well, just not quite as strongly.
But any reasonable formula I can imagine for choosing the most strategic vote under Score (or approval or choose one) that had access to what other voter's affinities were, would attempt to convert those affinities to votes in the process. That's why my vote simulator did that in an iterative process.
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@rob In principle, this is an infinite recursion. To predict how they will vote, you have to model their prediction of how you will vote. Where do you stop?
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Making Voters Equal in Power:
In principle, this is an infinite recursion.
And hence, "hall of mirrors."
In practice, my iterative vote simulator stops when the ordering of candidates doesn't change between two rounds. Since the ordering is all the "vote caster" algorithm looks at, there is no point continuing because it will always get the same result.
But keep in mind, that doesn't mean it has reached the one and only equilibrium. There can be multiple equilibria.
But again, I'd rather have a method that doesn't encourage this sort of thing. If I did a vote simulator for Condorcet, there would be very little, if any, iterating, since there isn't an obvious way to adjust your ballot even if you know how others will vote.
