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Gibbard's theorem shows that any strategyproof game form (i.e. one with a dominant strategy) with more than two outcomes is dictatorial. The Gibbard–Satterthwaite theorem is a special case showing that no deterministic voting system can be fully invulnerable to strategic voting in all circumstances, regardless of how others vote.
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 ...
The Gibbard–Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 [ 1 ] and then proved independently by the philosopher Allan Gibbard in 1973 [ 2 ] and economist Mark Satterthwaite in 1975. [ 3 ]
Gibbard and Satterthwaite give an impossibility result similar in spirit to Arrow's impossibility theorem. For a very general class of games, only "dictatorial" social choice functions can be implemented.
Arrow's impossibility theorem [61] and the Gibbard–Satterthwaite theorem prove that any useful single-winner voting method based on preference ranking is prone to some kind of manipulation. Game theory has been used to search for some kind of "minimally manipulable" (incentive compatibility) voting schemes. Game theory can also be used to ...
A Catholic nun was arrested by Italian police on Thursday for bringing messages for the mafia to prisoners, police said in a news statement. Sister Anna Donelli acted on several occasions as an ...
Sen's proof, set in the context of social choice theory, is similar in many respects to Arrow's impossibility theorem and the Gibbard–Satterthwaite theorem. As a mathematical construct, it also has much wider applicability: it is essentially about cyclical majorities between partially ordered sets, of which at least three must participate in ...
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