The Gibbard–Satterthwaite theorem, named after Allan Gibbard and Mark Satterthwaite, is a result about the deterministic voting systems that choose a single winner using only the preferences of the voters, where each voter ranks all candidates in order of preference. The Gibbard–Satterthwaite theorem states that, for three or more candidates, one of the following three things must hold for every voting rule:

1. The rule is dictatorial (i.e., there is a single individual who can choose the winner), or
2. There is some candidate who can never win, under the rule, or
3. The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his or her preferences.