Gibbard–Satterthwaite theorem

From Freepedia

The Gibbard–Satterthwaite theorem is a result about voting systems designed to choose a single winner from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that, for three or more candidates, one of the following three things must hold for every voting rule:

1. The rule is dictatorial, or
2. There is some candidate who cannot win, under the rule, in any circumstances, or
3. The rule is manipulable (i.e. susceptible to tactical voting), in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to, by voting in a manner that does not reflect his preferences, ensure the victory of a candidate whom the voter prefers to the candidate the rule would generate if the voter revealed his true preferences.

Since rules which forbid certain candidates from winning or which are dictatorial are not suitable for real-life voting systems, all such systems either are manipulable or do not meet the preconditions of the theorem.

Arrow's impossibility theorem is a similar theorem that deals with systems designed to yield a complete preference order of the candidates, rather than only choosing a winner.

External Links

• The Proof of the Gibbard–Satterthwaite Theorem Revisited
• Arrow’s Theorem and the Gibbard–Satterthwaite Theorem: A Unified Approach