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  2. Gibbard–Satterthwaite theorem - Wikipedia

    en.wikipedia.org/wiki/GibbardSatterthwaite...

    The Gibbard–Satterthwaite theorem is a theorem in social choice theory.It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 [1] and then proved independently by the philosopher Allan Gibbard in 1973 [2] and economist Mark Satterthwaite in 1975. [3]

  3. Gibbard's theorem - Wikipedia

    en.wikipedia.org/wiki/Gibbard's_theorem

    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 ...

  4. Proof of impossibility - Wikipedia

    en.wikipedia.org/wiki/Proof_of_impossibility

    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.

  5. Social choice theory - Wikipedia

    en.wikipedia.org/wiki/Social_choice_theory

    The Gibbard–Satterthwaite theorem implies that the only rule satisfying non-imposition (every alternative can be chosen) and strategyproofness when there are more than two candidates is the dictatorship mechanism. That is, a voter may be able to cast a ballot that misrepresents their preferences to obtain a result that is more favorable to ...

  6. Mechanism design - Wikipedia

    en.wikipedia.org/wiki/Mechanism_design

    Mechanism design, sometimes called implementation theory or institution design, [1] is a branch of economics, social choice, and game theory that deals with designing game forms (or mechanisms) to implement a given social choice function.

  7. Regret-free mechanism - Wikipedia

    en.wikipedia.org/wiki/Regret-free_mechanism

    This means that, for 3 or more outcomes, the only RFTT mechanisms are dictatorships (by the Gibbard–Satterthwaite impossibility theorem); and for 2 outcomes, a mechanism is RFTT if and only if it is an extended majority rule. As an example, to see that plurality voting is not RFTT for 3 outcomes, suppose an agent's preference ranking is z>y>x.

  8. The End of the Voting Methods Debate - AOL

    www.aol.com/news/end-voting-methods-debate...

    It has been proven (Gibbard-Satterthwaite theorem, as extended) that every voting method (other than a dictatorship) can be manipulated to some extent by strategic voting. No voting method can be ...

  9. Strategic voting - Wikipedia

    en.wikipedia.org/wiki/Strategic_voting

    Arrow's impossibility theorem [61] and the Gibbard–Satterthwaite theorem prove that any useful single-winner voting method based on preference ranking is prone to some kind of manipulation. Game theory has been used to search for some kind of "minimally manipulable" (incentive compatibility) voting schemes. Game theory can also be used to ...