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Thank you for pointing out how overused "Arrow's impossibility theorem" is as an argument against all voting systems (and therefore often as an argument against

Thank you for pointing out how overused "Arrow's impossibility theorem" is as an argument against all voting systems (and therefore often as an argument against all reforms to the current near-worst possible voting system). I would go further and be somewhat dismissive even of "Gibbard's theorem", since it only shows that an insincere vote can strategically produce a better outcome for a voter if they can identify what that that vote should be, and if they are one of the voters for whom such a strategy is available. So it doesn't guarantee (as far as I'm aware) that even a single voter (under every possible cardinal voting system) will necessarily have enough information before or during the election to confidently pick some specific insincere vote that will increase their chances of getting the outcome they want.

naniwaduni 4y ago
> I would go further and be somewhat dismissive even of "Gibbard's theorem", since it only shows that an insincere vote can strategically produce a better outcome for a voter if they can identify what that that vote should be, and if they are one of the voters for whom such a strategy is available. Gibbard's theorem is even weaker than that. It only assures the constructibility of vote sets for which the right "final" votes to achieve a particular outcome are distinct. It does not guarantee that there are any insincere votes which perform better than a sincere vote! Optimal strategic approval voting with a strict ordering is always a choice between sincere votes, in fact (since adding a vote for a strictly more preferred candidate never hurts your preferences, you can always find a sincere vote which performs better than an insincere strategic vote by additionally voting for all candidates more preferred than the least preferred candidate on the strategic vote).

naniwaduni 4y ago

> I would go further and be somewhat dismissive even of "Gibbard's theorem", since it only shows that an insincere vote can strategically produce a better outcome for a voter if they can identify what that that vote should be, and if they are one of the voters for whom such a strategy is available. Gibbard's theorem is even weaker than that. It only assures the constructibility of vote sets for which the right "final" votes to achieve a particular outcome are distinct. It does not guarantee that there are any insincere votes which perform better than a sincere vote! Optimal strategic approval voting with a strict ordering is always a choice between sincere votes, in fact (since adding a vote for a strictly more preferred candidate never hurts your preferences, you can always find a sincere vote which performs better than an insincere strategic vote by additionally voting for all candidates more preferred than the least preferred candidate on the strategic vote).