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Otherwise, the other voters use a classic voting rule, for example the Borda count. This game form is clearly dictatorial, because voter 1 can impose the result. However, it is not strategyproof: the other voters face the same issue of strategic voting as in the usual Borda count. Thus, Gibbard's theorem is an implication and not an equivalence.
Some voting rules are difficult to explain to voters in a way they can intuitively understand, which may undermine public trust in elections. [8] [failed verification] For example, while Schulze's rule performs well by many of the criteria above, it requires an involved explanation of beatpaths. Ease of voting.
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 ...
Like all (deterministic, non-dictatorial, multicandidate) voting methods, rated methods are vulnerable to strategic voting, due to Gibbard's theorem. Cardinal methods where voters give each candidate a number of points and the points are summed are called additive. Both range voting and cumulative voting are of this type.
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]
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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.