Search results
Results from the WOW.Com Content Network
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]
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 ...
The median rule apparently contradicts this theorem, because it is strategyproof and it is not a dictatorship. In fact there is no contradiction: the Gibbard-Satterthwaite theorem applies only to rules that operate on the entire preference domain (that is, only to voting rules that can handle any set of preference rankings).
Gibbard's theorem shows that no deterministic single-winner voting method can be completely immune to strategy, but makes no claims about the severity of strategy or how often strategy succeeds. Later results show that some methods are more manipulable than others.
Mechanism design (sometimes implementation theory or institution design) [1] is a branch of economics and game theory. It studies how to construct rules—called mechanisms or institutions—that produce good outcomes according to some predefined metric , even when the designer does not know the players' true preferences or what information ...
This work would eventually become known as "Gibbard's theorem", published in 1973. [2] Mark Satterthwaite later worked on a similar theorem which he published in 1975. [8] [9] Satterthwaite and Jean Marie Brin published a paper in 1978 describing Gibbard's and Satterthwaite's mathematical proofs as the "Gibbard–Satterthwaite theorem" and ...
[1] [2] [3] Sen's proof, set in the context of social choice theory, is similar in many respects to Arrow's impossibility theorem and the Gibbard–Satterthwaite theorem. As a mathematical construct, it also has much wider applicability: it is essentially about cyclical majorities between partially ordered sets, of which at least three must ...
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism (such as an electoral system or market). [1] It can be seen as a kind of mirror image to Gibbard's theorem.