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In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. [1] It states that for any deterministic process of collective decision, 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 ...
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 ...
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]
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. [1] Social choice studies the behavior of different mathematical procedures (social welfare functions) used to combine individual preferences into a coherent whole.
Condorcet's jury theorem shows that so long as p > 1 ⁄ 2, the majority vote of a jury will be a better guide to the relative merits of two candidates than is the opinion of any single member. Peyton Young showed that three further properties apply to votes between arbitrary numbers of candidates, suggesting that Condorcet was aware of the ...
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 median voter theorem relates to ranked voting mechanisms, in which each agent reports his/her full ranking over alternatives. The theorem says that, if the agents' preferences are single-peaked , then every Condorcet method always selects the candidate preferred by the median voter (the candidate closest to the voter whose peak is the ...