Asymptotical Strategy-Proofness of Scoring Methods

A well-known impossibility theorem in social choice theory states that every non-dictatorial social choice function, assigning a unique alternative from a set of at least three to every profile of individual preferences, can be manipulated. In this paper we examine a particular family of social choice functions, the scoring functions, and show that the failure frequency of such functions, understood as the relative frequency of profiles for which the social choice is undefined or can be manipulated, goes to zero as the number n of individuals becomes large. Moreover, the rate of convergence can be established as n(raised to the -1/2 power).