Paradox of Voting

The paradox of voting, also called Downs’ paradox, is that for a rational, self-interested voter, the costs of voting will normally exceed the expected benefits. The act of voting involves a benefit and a cost to the voter. A benefit is derived if the voter changes the outcome of the election to the one that is desired (in such a case, the voter is said to be pivotal). The probability of this happening is very low so the expected benefit is small. Because the chance of exercising the pivotal vote is minuscule compared to any realistic estimate of the private individual benefits of the different possible outcomes, the expected benefits of voting are less than the costs. Anthony Downs presents this rational calculus of voting in his treatise ‘An Economic Theory of Democracy’ published in 1957.

Responses to the paradox have included the view that voters vote to express their preference for a candidate rather than affect the outcome of the election and that voters exercise some degree of altruism. The issue was noted by Nicolas de Condorcet in 1793 when he stated, “In single-stage elections, where there are a great many voters, each voter’s influence is very small. It is therefore possible that the citizens will not be sufficiently interested [to vote].”

In 1821, Hegel made a similar observation in his Elements of the Philosophy of Right: “As for popular suffrage, it may be further remarked that especially in large states it leads inevitably to electoral indifference, since the casting of a single vote is of no significance where there is a multitude of electors.”

Alternative responses modify the postulate of egoistic rationality in various ways. For example, Geoffrey Brennan and Loren Lomasky suggest that voters derive “expressive” benefits from supporting particular candidates – analogous to cheering on a sports team – rather than voting in hopes of achieving the political outcomes they prefer.

Some argue that the paradox appears to ignore the collateral benefits associated with voting, besides affecting the outcome of the vote. For instance, magnitudes of electoral wins and losses are very closely watched by politicians, their aides, pundits and voters, because they indicate the strength of support for candidates, and tend to be viewed as an inherently more accurate measure of such than mere opinion polls (which have to rely on imperfect sampling). Another argument that has been raised is that researching who or what to vote for may increase the voter’s political knowledge and community awareness, both of which may contribute to a general sense of civic duty, although in such a case the act of voting itself contributes nothing to this.

One paradox of voting states that, in a general election, in which many citizens vote, the probability that a single voter can affect the outcome is so small that citizens in general have no rational reason for voting. However, if all citizens accept this reasoning, then none will vote, and so each vote has a large probability of affecting the outcome. Hence all should vote after all.