Downs' paradox of voting is the puzzle that instrumental rational-choice reasoning often predicts abstention even though people vote. If $p$ is the probability that one vote changes the outcome, $B$ is the benefit of the preferred candidate winning, and $C$ is the cost of voting, the instrumental payoff is $pB-C$. Because $p$ is usually very small, this payoff may be negative, making participation difficult to explain using self-interest alone.