Gibert-Saththwaite theorem

Maskin monotonicity is a loosening of [strategicity

The Gibbard-Sutterthwaite theorem is the theorem that when society's preferences are determined by voting among three or more candidates, the only social choice rule that does not exclude a particular candidate and satisfies the strategy-resistant property is autocracy. Alan Gibbard and Mark Satterthwaite (English version) gave this theorem. Here,

Elimination of a particular candidate refers to the case where there is a candidate who will not be elected under any voting result.

Strategic resistance means that none of the participants has an incentive to engage in strategic manipulation (i.e., individuals participating in the voting process falsely expressing their own preferences to achieve a more desirable outcome for themselves).

A dictatorship is a rule where there is one particular individual (the dictator) and the first choice for the dictator becomes the decision of society, no matter what the preferences of the other participants are.

According to this theorem, in a vote where more than three people can be elected, it is inevitable that participants will vote for the next best (in a sense false) proposal so that their vote will not be a dead vote, unless it is a dictatorship.

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