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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 ...
Gibbard's proof of the theorem is more general and covers processes of collective decision that may not be ordinal, such as cardinal voting. [note 1] Gibbard's 1978 theorem and Hylland's theorem are even more general and extend these results to non-deterministic processes, where the outcome may depend partly on chance; the Duggan–Schwartz ...
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.
Arrow's theorem does not cover rated voting rules, and thus cannot be used to inform their susceptibility to the spoiler effect. However, Gibbard's theorem shows these methods' susceptibility to strategic voting, and generalizations of Arrow's theorem describe cases where rated methods are susceptible to the spoiler effect.
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. [1] Gibbard's theorem shows that no voting system has a single "always-best" strategy, i.e. one that always maximizes a voter's satisfaction with the result, regardless of other ...
The revelation principle shows that, while Gibbard's theorem proves it is impossible to design a system that will always be fully invulnerable to strategy (if we do not know how players will behave), it is possible to design a system that encourages honesty given a solution concept (if the corresponding equilibrium is unique). [3] [4]
Gibbard's theorem, built upon the earlier Arrow's theorem and the Gibbard–Satterthwaite theorem, to prove that for any single-winner deterministic voting methods, 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 highest median voting rules are a class of graded voting rules where the candidate with the highest median rating is elected.. The various highest median rules differ in their treatment of ties, i.e., the method of ranking the candidates with the same median rating.