 For instance, one early hypothesis was that voting might be a form of insurance, meant to to prevent democracy from collapsing (Downs 1957: 257). Following this suggestion, suppose one hypothesizes that citizens have a duty to vote in order to help prevent democracy from collapsing. Suppose there is some determinate threshold of votes under which a democracy becomes unstable and collapses. The problem here is that just as there is a vanishingly small probability that any individual’s vote would decide the election, so there is a vanishingly small chance that any vote would decisively put the number of votes above that threshold. Alternatively, suppose that as fewer and fewer citizens vote, the probability of democracy collapsing becomes incrementally higher. If so, to show there is a duty to vote, one would first need to show that the marginal expected benefits of the nth vote, in reducing the chance of democratic collapse, exceed the expected costs (including opportunity costs).