An application of binomial coefficients to Social Choice Theory

Abstract

In this paper we determine the number of positive integer sequences a1, a2, . . . , ak such that 1 ≤ a1 ≤ · · · ≤ ak ≤ m and ai ≥ i for all i ∈ {1, . . . , k}. After that, we apply this result to calculate the number of anonymous, neutral and monotonic social welfare functions when only two alternatives are considered.