Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof

Abstract

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is gdescribable.h The gdescribableh coalitions are assumed to form a countable Boolean algebra. The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society. The discussion clarifies within a single framework a connection between the negative result (the Gibbard-Satterthwaite theorem) for finite societies and the positive result for infinite ones.Gibbard-Satterthwaite theorem, cheatproofness, dominant strategy implementation, strategy-proof social choice functions, plurality rule, infinitely large societies, countable Boolean algebras of coalitions, free ultrafilters, models of knowledge, partitional information functions.