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Is there a voting method where the best strategy for strategic voters can be explained in a sane way?

According to Gibbard–Satterthwaite, there is no "strategy-free" (and reasonable) voting method. That is, if "honesty is the best policy" for a voting method, then the voting method must ignore the voters or be non-deterministic.

Strategic voting in plurality is often pretty simple: amongst those candidates that have a chance of winning, vote for your favorite. So vote nearly honestly, but generally avoid third party candidates.

However, violations of the monotonicity criterion and participation criterion are pretty irritating for describing a good "strategy" for lying on the ballot. In particular, you can cause a winner to lose by voting for them, and you can cause a loser (that you would have voted for) to win by not voting. In the presence of these "if you try to help, you can hurt" conditions, it seems almost impossible to formulate the winning strategy for a strategic voter.

On the other hand, some fairness criteria do not seem tuned to making strategies easy, so perhaps those criteria and the associated impossibility theorems could be ignored.

Is there a voting method where the best strategy for strategic voters can be explained in a sane way?

I assume there is no such strategy for plurality with elimination, but perhaps I am wrong and am just distracted by monotonicity.

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It's not even clear to me what it would mean that a voting strategy is "best". Presumably one could assign utility values to each possible outcome and seek the highest expected utility, but that doesn't begin to capture the fact that the practical worth of a strategy depends on assumptions about what other voters' utility assignments are and which strategies they choose. –  Henning Makholm Sep 2 '11 at 23:00
    
@Henning Makholm: I'm imagining that we have at least a decent idea of other's voters utility (so people lie on election day, but not to the polls). I'm not sure what sort of assumptions on strategies would be reasonable. Highest expected utility requires we know the other voters' strategies, right? not just their utility. It does seem a little circular. –  Jack Schmidt Sep 2 '11 at 23:12
    
Yes. There are game-theoretic swamps and marshes to lose oneself in here. And since it isn't even zero sum, without some restrictions on the voting method, it could work out to reproduce the prisoners' dilemma, and we'd need to solve the entire problem of the social origin of mutual trust and collaboration before we could make a rational choice... –  Henning Makholm Sep 2 '11 at 23:30
    
This is a great question! One of the assumptions in social choice theory is that interpersonal utilities can't be compared, so when we talk about solution concepts (say Pareto or Condorcet or core), we consider only ordinal preferences. If there is only one or a top cycle of these solution concepts, it's possible to denote voting methods and "sane" strategies given a structure on the preferences and common knowledge among participants. You should consider asking this on a Game Theory StackExchange –  Merbs Nov 30 '12 at 12:26
    
But if you imagine just a simple cycle (one person prefers $A>B>C$, another $B>C>A$ and the third $C>A>B$) such that the group prefers $A>B>C>A$, then the voting method (say a particular agenda) dictates the strategic voting (via backward induction) as well as the outcome. So (1) it's not that there aren't "sane" strategies for many popular voting methods, (2) for many people, telling the truth may be that "sane" strategy, and (3) the less information people have, the less strategic they can be, so the truth may be the best you can vote. –  Merbs Nov 30 '12 at 12:37

2 Answers 2

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Part of the issue here is what "level" of information you might have available about how other voters are going to vote. A very informative book about manipulation of voting systems is Social Choice and the Mathematics of Manipulation by Alan Tayler, Cambridge U. Press, 2005.

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Bad timing on my part, I suppose, but all nearby libraries with the book are closed until Monday or Tuesday. Can you give an example? This is pedagogical, so basically anything that makes sense is a valid answer. I've discussed sane strategic voting for plurality, and the insanity for P w/ E, but I'm lost on providing any other example of sane strategic voting. As my student said "so it's just random?" and I replied "No it's just very hard." –  Jack Schmidt Sep 2 '11 at 22:50
    
I've added the book to ILL as the table of contents seems good, but the ebrary preview is of two blank pages per part... so i've got no idea if its the right book for me. Aha, but the Amazon preview looks very good. +1 at the very least for a useful reference. –  Jack Schmidt Sep 2 '11 at 22:51
    
@Jack You can find out more about this issue (strategic/tactical voting) at these two web sites: wiki.electorama.com/wiki/Tactical_voting and rangevoting.org/RangeVoting.html –  Joseph Malkevitch Sep 3 '11 at 15:16

You might want to check out range voting. Range voting is like approval voting, where You can vote for as many Candidates as You like except, while in approval voting You say, "I approve or disapprove of these Candidates", under range voting You say, "I give these Candidate X out of 10 votes, those Candidate Y out 10, and this Candidate Z out of 10 votes." (Note: Range voting is note like simply having multiple votes where You are given, for example, 10 votes and told to allocate them amongst different Candidates. Instead, range voting is more like a movie rating system: 4 out of 5 stars, for example.) Range voting lets People vote for Whom They like while encouraging Them to vote honestly.

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