Gibbard's theorem
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English[edit]
Etymology[edit]
Proven by philosopher Allan Gibbard in 1973.
Proper noun[edit]
- 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[edit]
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.