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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 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.
Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [48] Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not ...
Noether's theorem (Lie groups, calculus of variations, differential invariants, physics) Noether's second theorem (calculus of variations, physics) Noether's theorem on rationality for surfaces (algebraic surfaces) Non-squeezing theorem (symplectic geometry) Norton's theorem (electrical networks) Novikov's compact leaf theorem
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 ]
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Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [11] and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance. The Gibbard's theorem assumes the collective decision results in exactly one winner ...