A Solution to the Problem of Mass Elections

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 RN, the sincere outcome F(RN) is also the outcome of some strong equilibrium point of the voting game determined by F and RN. 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.