Gibbard's theorem

English

Etymology

Proven by philosopher Allan Gibbard in 1973.

Proper noun

Gibbard's theorem

1. A theorem stating that, for any deterministic process of collective decision, at least one of the following three properties must hold: (i) the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; (ii) the process limits the possible outcomes to two options only; (iii) the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

Usage notes

The main difference between this and the Gibbard-Satterthwaite theorem is that the latter is limited to ranked (ordinal) voting rules: a voter's action consists in giving a preference ranking over the available options. Gibbard's theorem is more general, including for example systems where voters assign grades to candidates.

Related terms

• Gibbard-Satterthwaite theorem