Paradox of voting

From Wikipedia, the free encyclopedia

Voting Part of a series of articles on Politics and Elections

Absentee ballot Abstention Ballot Ballot box Ballot stuffing Early voting Election Day Registration Election threshold Elector None of the above Paradox of voting Polling station Postal voting Precinct Preference vote Protest vote Provisional ballot Refused ballot Secret ballot Spoilt vote Tactical voting Tally (voting) Ticket (election) Ticket splitters Vote center Vote pairing Voter fatigue Voter registration Voter turnout Voting booth Voting machine
Politics Portal · edit

The paradox of voting, also referred to as Downs paradox is a reference to the fact that for a rational, self-interested voter, the costs of voting will normally exceed the expected benefits. Because the chance of exercising a decisive vote (i.e. the chance of a tied election) is tiny 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. The fact that people do vote is a major problem for public choice theory, first observed by Anthony Downs ^[1].

1 Illustration
2 Responses
3 See also
4 Notes

[edit] Illustration

As a first approximation, it seems reasonable to argue that the likelihood of voter x being decisive, that is, of the vote being tied in the absence of voter x is of the order of ¹⁄_n where n is the number of voters. In a typical United States presidential election, n will be of the order of 100 million. On the other hand, the benefit to an individual voter of one p winning, rather than the other, is presumably smaller than the individual's personal wealth which for most people is less than $1 million. So, the expected benefit of voting is less than 1 cent for any given person, much less than the cost of turning out to vote.

On the assumption of rational egoism, the number of participants in an election should decline to the point where the expected benefit of voting is equal to the cost. In the example above, if the cost of voting is $1, this point would be achieved if turnout fell to 1 per cent.

[edit] Responses

One possible response to the paradox of voting is to argue that the probabiltiy of being decisive is much larger than ¹⁄_n. It has been argued that if each individual voter is equally likely to vote either way then the binomial distribution yields a probability of a tie of the order of $\textstyle\frac{1}{\sqrt{n}}$ , where n is the number of voters . Unfortunately, this approach also implies that the result of, say, a US presidential election can be known, with virtual certainty, to within a few thousand votes. More realistic models yields a probability that is somewhat larger than ¹⁄_n, but still very small.

Alternative responses modify the postulate of egoistic rationality in various ways. For example, Brennan and Lomasky suggest that voters derive 'expressive' benefits from supporting particular candidates.^{[citation needed]} However, this implies that voting choices are unlikely to reflect the self-interest of voters, as is normally assumed in public choice theory, i.e., rational behavior is restricted to the instrumental as opposed to the intrinsic value of actions.

Some have hypothesized that voting is linked genetically with evolved behaviors such as cooperation. One study of identical and fraternal twins' voting patterns concluded that 60% of differences in turnout among twins can be accounted for by genetics, but another interpretation of this study put the figure at 40%.^[2]