A Solution to the Problem of Mass Elections

Abstract

We shall review a solution to the problem of mass elections which has been developed during the past ten years. I have both existence and uniqueness results. Our approach is axiomatic in the following sense. We consider the following properties of social choice functions: (i) anonymity; (ii) Pareto-optimality; (iii) monotonicity; and (iv) exact and strong consistency. Properties (i)-(iii) are well-known. Property (iv) is defined as follows. A social choice function F is exactly and strongly consistent if, for each profile of true preferences R^N, the sincere outcome F(R^N) is also the outcome of some strong equilibrium point of the voting game determined by F and R^N. Let ϕ) be the set of all social choice functions that satisfy (i)-(iv) and let F ∈ ϕ. Because F is anonymous and Pareto-optimal, the size of a minimal winning coalition with respect to F, k(F), is well-defined. Finally, F_* is a solution to the problem of mass elections if F_* ∈ ϕ and k(F_*) ≤ k(F) for all F ∈ ϕ. Thus our solution is defined by axioms (i) to (iv) and the foregoing minimality condition.