In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:
- The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
- The process limits the possible outcomes to two options only.
- The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots.
A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite applies only to ranked voting. Because of its broader scope, Gibbard's theorem makes no claim about whether voters need to reverse their ranking of candidates, only that their optimal ballots depend on the other voters' ballots.
