No rational egoist should bother voting because, as Skinner's Dr. Frazier notices, the probability of any one man casting the decisive ballot “is less than the chance he will be killed on the way to the polls.” No matter how deeply he cares about the electoral outcome, a man must realize that his vote is only one among very many. The larger the electorate, the smaller the probability of any one vote's changing the outcome, so in most modern polities the politically rational thing to do is to conserve on shoe leather.
Real-world voters, of course, do flock to the polls, which is usually explained in terms of a feeling of “civic duty.” The fact that men get some satisfaction from discharging their civic duty by voting might answer the question of why it is rational for them to go to the polls. Unfortunately, it leaves another—how do they vote once they get there? Presumably, they go ahead and vote according to the dictates of their egoistic interests.