A simple proof of Suzumura's extension theorem for finite domains with applications.
A stochastic model of choice.
An approach to choice function theory is suggested which is probabilistic and non-deterministic. In the framework of this approach fuzzy choice functions are introduced and a number of necessary and sufficient conditions for a fuzzy choice function to be a fuzzy rational choice function of a certain type are established.
A tight quantitative version of Arrow’s impossibility theorem
The well-known Impossibility Theorem of Arrow asserts that any generalized social welfare function (GSWF) with at least three alternatives, which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a dictatorship, is necessarily non-transitive. In 2002, Kalai asked whether one can obtain the following quantitative version of the theorem: For any , there exists such that if a GSWF on three alternatives satisfies the IIA condition and its probability of non-transitive...