Optimal enfranchisement

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 highest stakes, with a smaller franchise when the stakes are more concentrated. When they are i.i.d. (all voters independently favour Yes 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 those 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 making the right decision. This helps to shed light on the problem in large populations.