At 03:57 PM 1/18/2009, Kristofer Munsterhjelm wrote:
Wouldn't it be stricter than this? Consider Range, for instance. One would guess that the best zero info strategy is to vote Approval style with the cutoff at some point (mean? not sure).
Actually, that's a lousy strategy. The reason it's lousy is that the voter is a sample of the electorate. Depending on the voter's own understanding of the electorate, and the voter's own relationship with the electorate, the best strategy might be a bullet vote. Saari showed why "mean cutoff" is terrible Approval strategy. What if every voter agrees with you but one? The one good thing Saari shows is that this yields a mediocre outcome when 9999/10000 voters prefer a candidate, but also approve another "above the mean."
Essentially, the voter doesn't need to know anything specific about the electorate in a particular election, but only about how isolated the voter's position *generally* is.
For most voters, zero-knowledge indicates a bullet vote unless there are additional candidates with only weak preference under the most-preferred one, such that the voter truly doesn't mind voting for one or more of them in addition.
However, it would also be reasonable that a sincere ratings ballot would have the property that if the sincere ranked ballot of the person in question is A > B, then the score of B is lower than that of A; that is, unless the rounding effect makes it impossible to give B a lower score than A, or makes it impossible to give B a sufficiently slightly lower score than A as the voter considers sincere (by whatever metric).
Yes. Indeed, I've suggested that doing pairwise analysis on Range ballots, with a runoff when the Range winner is beaten by a candidate pairwise, would encourage maintenance of this preference order.
Think of Range as a Borda ballot with equal ranking allowed and therefore with empty ranks. (Not the ridiculous suggestions that truncated ballots should be given less weight). If a voter really has weak preference between two candidates, the obvious and simple vote is to equal rank them. But then where does one put the empty rank?
There are two approaches, and both of them are "sincere," though one approach more accurately reflects relative preference strength. There are ways to encourage that expression.
But here is the real problem: trying to think that a zero-knowledge ballot is somehow ideal is discounting the function of compromise in elections. That is, what we do in elections is *not only* to find some sort of supposed "best" candidate, but also to find compromises. That's what we do in deliberative process where repeated Yes/No voting is used to identify compromises, until a quorum is reached (usually a majority, but it can be supermajority). Deliberative process incorporates increasing knowledge by the electorate of itself. It extracts this with a series of elections in which sincerity is not only expected, it's generally good strategy. In that context, "approval" really is approval! If a majority agrees with your approval, the process is over.
I consider election methods as shortcuts, attempts to discover quickly what the electorate would likely settle on in a deliberative environment. As such, it is actually essential that whatever knowledge the electorate has of itself be incorporated into how the voters vote.
And that's what happens if, in a Range election, voters vote von Nuemann-Morganstern utilities. They have one full vote to "bet." They put their vote where they think it will do the most good. They can put it all on one candidate, i.e., bullet vote. They can put it on a candidate set, thus voting a full vote for every member of the set over every nonmembe, i.e., they vote Approval style. They can split up their vote in more complex ways. What they can't do in this setup is to bet more than one vote. I.e., for example, one full vote for A over B, and one full vote for B over C. If we arrange their votes in sequence, from least preferred to most, the sum of votes in each sequential pairwise election must total to no more than one vote.
Calling them VNM utilities sounds complex, but it's actually instinctive. If we understand Range, we aren't going to waste significant voting power expressing moot preferences. Suppose someone asks you what you want. But you understand that you might not get what you want. You prefer A>B>C>D, lets say with equal preference steps. You think it likely that A or B might be acceptable to your questioner, but not C or D. You have so much time to convince your questioner to give you what you argue for. How much time are you going to spend trying to convince the person to give you C instead of D?
You might mention it, but you wouldn't put the weight there unless you thought that the real possibilities were C or D.
Voter knowledge of the electorate is how elections reach compromise, and it's very important. Of course, there is also the process for getting on the ballot, in some places, but where ballot access is easy, it's about the only way we have in single-winner elections of finding an acceptable compromise.
That's not to deny the value of voting systems which can extract a probably reasonable compromise from expressed preferences, but one of my points has been that unless preference strength *can* be expressed, we are presenting distorted information to the voting system.
At least the voters should be able to "distort" as they choose, seeking compromise, instead of the system inherently distorting.... we know that some voters will simply vote as accurately as they can and, it turns out, from at least one study (mine) this tends to improve expected results for all the voters,
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