A Fourier-theoretic perspective on the Condorcet paradox and Arrow's theorem. (Q1866178)

A social choice function is rational if it is an order on the alternatives; it is symmetric if the choice is invariant under some transitive group of permutations of the voters (not necessarily all permutations). The main result of the paper is that, as the number of voters tends to infinity, the probability that a symmetric social choice function on three alternatives gives a rational outcome is bounded above by 0.9192. The bound is determined via computation of Fourier coefficients. The author also provides a proof of Arrow's theorem using the same techniques and discusses a number of applications and conjectures, as well as problems generalizing the results to cases with more alternatives.