On Jan 8, 2009, at 4:45 PM, Abd ul-Rahman Lomax wrote:
The whole concept of strategic voting is flawed when applied to Range. Voters place vote strength where they think it will do the most good -- if they think. Some don't. Approval is essentially, as Brams claimed, "strategy-free," in the old meaning, and the only way that it was at all possible to call it vulnerable was that critics claimed that there was some absolute "approval" relation between a voter and a candidate.
It would be useful to generalize the concept of strategic voting (and the related concepts of manipulation and sincerity) to other than linear ballots (that is, a ballot with an ordinal ranking of the voter's preferences). With linear ballots (and so Borda, IRV and various Condorcet methods) we define a "sincere" ballot as the one a voter would cast if the voter were a dictator, and manipulability as the ability of a voter to achieve a better result (where "better" means the election of a candidate ranked higher on that voter's sincere ballot) by voting "insincerely" or "strategically"--that is, by casting a ballot different from their sincere ballot. An election method that is not manipulable in this sense is defined to be "strategy-free".
A two-candidate plurality election is strategy-free. Most interesting elections are not.
With any practical election method using linear ballots, manipulation cannot succeed unless the voter has knowledge of how the other voters are voting. This knowledge need not be perfect. I propose (and I don't claim that this is original, though I don't recall seeing the definition) that we use this observation to generalize the idea of manipulability to election methods, such as Range and Approval, that do not use linear ballots, thus:
An election method is manipulable if a voter has a rational motivation to cast different ballots depending on the voter's knowledge (or belief) of the ballots of other voters.
In such an election, a voter should vote strategically when the ballot that will produce the "best" outcome (for that voter) depends on the behavior of the other voters, the strategy consisting of determining, by some means depending on the method, which ballot that is.
For example, in an Approval election, with a preference of A>B>C, we will always vote for A, but whether we vote for B depends on how well we believe B and C are doing with other voters. If we believe that C cannot win, then we vote for A only, to improve our chance of electing A over B. If we believe that C is a serious threat, then we vote for A and B, to improve our chance of rejecting C.
The generalization of a "sincere" ballot then becomes the zero- knowledge (of other voters' behavior) ballot, although we might still want to talk about a "sincere ordering" (that is, the sincere linear ballot) in trying to determine a "best possible" outcome.
It seems to me that it's clearly desirable to be able to optimize the outcome by casting a sincere linear ballot. Such a ballot is reasonably expressive (that is, it contains more information about my preferences than, say, a plurality or approval ballot) without (in itself) requiring me to strategize. Unfortunately, no such election method exists, and many (most?) of the arguments on this list are over the tradeoffs implied by that sad fact. The best we can do is to find a method in which it's very unlikely that we can improve our outcome by voting other than sincerely.
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