Optimal Enfranchisement

Abstract

We study the optimal voting franchise for a decision which affects different persons with different intensities. When the agents' opinions are ex ante permutation invariant, we show that it is optimal to restrict the franchise to the agents with the higher stakes, with a smaller franchise when stakes are more concentrated. When they are i.i.d. (all voters favour Yes independently with the same probability p), we further show that two forces are at work: on the one hand, the imperative to restrict voting rights to the most affected; on the other, when and only when p ≠ 1/2, the Condorcet jury effect according to which allowing more voters to participate increases the probability of taking the right decision. This helps shed light on the problem in large populations.

Keywords: voting, democracy, enfranchisement, preference intensity