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Is it ever safe to vote strategically?

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Abstract:

There are many situations in which mis-coordinated strategic voting can leave strategic voters worse off than they would have been had they not tried to strategize. We analyse the simplest of such scenarios, in which the set of strategic voters all have the same sincere preferences and all cast the same strategic vote, while all other voters vote sincerely. Most mis-coordinations in this framework can be classified as instances of either strategic overshooting (too many voted strategically) or strategic undershooting (too few). If mis-coordination can result in strategic voters ending up worse off than they would have been had they all just voted sincerely, we call the relevant strategic vote unsafe. We show that under every onto and non-dictatorial social choice rule there exist circumstances where a voter has an incentive to cast a safe strategic vote. We extend the Gibbard-Satterthwaite Theorem by proving that every onto and non-dictatorial social choice rule can be individually manipulated by a voter casting a safe strategic vote.

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