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Gibbard's 1978 theorem states that a nondeterministic voting method is only strategyproof if it's a mixture of unilateral and duple rules. For instance, the rule that flips a coin and chooses a random dictator if the coin lands on heads, or chooses the pairwise winner between two random candidates if the coin lands on tails, is strategyproof.
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 ...
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 ...
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.
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.
On a rated ballot, the voter may rate each choice independently. An approval voting ballot does not require ranking or exclusivity. Rated, evaluative, [1] [2] graded, [1] or cardinal voting rules are a class of voting methods that allow voters to state how strongly they support a candidate, [3] by giving each one a grade on a separate scale.
The pandemic-era 2020 election had the highest ever early vote totals, at more than 101 million, or 63% of all votes cast. But beside 2020, the share of early votes has remained steady since 2012 ...
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]