Voting as a rational decision

Andrew Gelman, Noah Kaplan 05 April 2008

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About fifteen years ago, I attended a lecture by venerable pollster Mervyn Field, who told us that when he started in the business in the 1950s, there was a lot of concern about nonvoters. What was going on with these people who were too alienated to participate in society in this most basic way? But, recently, Field continued, the question has become, Who are these “voters”? What makes them tick? Who are these unsung heroes who make our democracy work by bothering to show up on election day?

Voter turnout is lower in the United States than in Europe. What would happen if all the Americans eligible to vote did so? According to opinion polls, nonvoters, when forced to declare a preference, are slightly more supportive of Democratic than Republican candidates, and Highton and Wolfinger (2001) estimate that, under 100% turnout, the Democrats would receive about 3 percentage points more of the national vote—not a lot, but enough to have swung the two most recent presidential contests. But election campaigns are not static. Jonathan Nagler and Jan Leighley (2007) show that nonvoters care about different issues than voters, and they conjecture that increased turnout would raise the profiles of these issues in the campaign. From the other direction, it has been argued that low turnout is a good thing, so that the election is decided by the most well-informed voters.

But what if voting is done not by the serious citizens, but rather the most foolish—or by the people who have nothing better to do on a Tuesday? This is what would seem to be implied by a straightforward decision-theoretic calculation. In the notation of Riker and Ordeshook (1968), the utility U gained from voting can be written as the sum of three terms,

U = p*B - C + D,

where p is the probability that your single vote is decisive, B is the benefit you gain from your preferred candidate winning the election, C is the cost incurred by going to the trouble to vote, and D is the direct benefit of voting irrespective of the outcome. C – D is the net cost of voting.

For a large election, the probability p can only be estimated as extremely small in any national election. A quick calculation: suppose there are 100 million voters choosing between two candidates, each of whom is expected to receive between 45% and 55% of the vote. The probability that your vote will swing the outcome of the election is then 1 in 10 million. (Analysis becomes more complicated when using real election forecasts for America’s two-stage presidential voting system, but the final number doesn’t change much.) Even for a benefit B that is fairly large, for example, $10,000, the product p*B is tiny. Given that the act of voting has a nonzero cost, voter turnout is thus usually attributed to some mix of irrationality, confusion, and the direct gratifications of voting (including the performance of a civic duty); that is, a negative net cost of the act of voting. However, these motivations do not explain observed variations in voter turnout between elections. In addition, voting is an act with large-scale consequences beyond any immediate satisfaction it gives to the voter. At the very least, many voters seem to consider their voting actions with more seriousness than other low-cost consumption decisions. This is why voter turnout has been called “the paradox that ate rational choice theory” (Fiorina, 1990, Green and Shapiro, 1994).

Rational voting

But here's the good news. If your vote is decisive, it will make a difference for tens of millions of people. If you think your preferred candidate could bring the equivalent of a $100 improvement in the quality of life to the average person in your country—not an implausible hope, given the size of national budgets and the impact of decisions in foreign policy, health, the environment, and other areas—you’re now buying a billion-dollar lottery ticket. With this payoff, a 1 in 10 million chance of being decisive isn't bad odds.

And many people do see it that way. Surveys show that voters choose based on who they think will do better for their country as a whole, rather than their personal betterment. Indeed, when it comes to voting, it is irrational to be selfish. The probability of your vote being decisive is roughly inversely proportional to the size of the electorate (see Gelman, King, and Boscardin, 1988, Gelman, Katz, and Bafumi, 2004, and Mulligan and Hunter, 2002, for details and empirical evidence), and your personal benefit remains flat, but the “social benefit”—the total gain for the country that you would anticipate, if your candidate wins—is proportional to the population, so that the product p*B approaches a constant, not zero, as the number of voters increases. (It is not necessary for this social benefit to be accurately perceived—see Caplan, 2007—for it to determine people’s votes.)

In “Voting as a rational choice: why and how people vote to improve the well-being of others,” co-authors and I show how this reasoning implies a feedback mechanism: if turnout declines, then the probability of a tied election increases, which in turn implies that, on the margin, it then becomes rational for some people to vote. The feedback with voter turnout is why voting is not a simple free-rider or prisoner’s dilemma problem: the more people who free ride (by not voting), the higher the expected benefit to you of voting, and so extremely low turnout is not an equilibrium.

In addition to predicting nontrivial turnout rates among rational voters, the model also explains the rationality of giving money to a candidate: Large contributions, or contributions to local elections, could conceivably be justified as providing access or the opportunity to directly influence policy. But small-dollar contributions to national elections, like voting, can be better motivated by the possibility of large social benefit than by any direct benefit to you. Such civically motivated behavior is consistent with both small and large anonymous contributions to charity. In two laboratory experiments on college students, Fowler (2006) and Fowler and Kam (2006) found that voters are more likely than nonvoters to behave altruistically (as is consistent with the social-benefit utility model) and display delayed-gratification behaviour (as is consistent with the fact that the costs of voting are immediate whereas the benefits are delayed).

The social motivation from voting also explains declining response rates in opinion polls. In the 1950s, when mass-opinion polling was rare, we would argue that it was more rational to respond to a survey than to vote in an election: as one of 1000 respondents in a national poll, there was a real chance that your response could noticeably affect the poll numbers (for example, changing a poll result from 49% to 50%). Nowadays, polls are so common that a telephone poll was done recently in the US to estimate how often individuals are surveyed (the answer was about once per year). It is unlikely that a response to a single survey will have much impact.

Thus far, we have primarily emphasised our theory as explaining the “mystery” that people vote. However, it also has implications for vote choices. Why you vote and how you vote are closely connected. If you are voting because of the possibility that you will decide the election and benefit others, then you will vote for the policy that you think will lead to the largest average benefit. There is no reason to vote for a policy that has idiosyncratic benefits to you because the individual-benefit term in your utility is essentially irrelevant for large electorates. This could be one reason why the rhetoric of politics tends to be phrased as benefits to society generally or to large deserving groups, rather than naked appeals to self-interest. No doubt many people are biased to think that what benefits them will benefit others, but we predict that most people will try to vote to benefit society at large or some large affinity group. Our contention therefore runs contrary to much of the political-economy work of the past few decades. Except in very small elections, a rational person who votes will choose the candidate or party with the best perceived social benefits to the population.

Rationality and selfishness

In surveys, voters say they are motivated by national conditions, and their turnout is consistent with this assumption, so perhaps we should believe them. Conversely, rational and purely selfish people should not vote. We have rescued rational choice theory from the voter turnout paradox, but at a price, by formally decoupling rationality from self-interest (except in the uninteresting tautological sense that anything you do must be in your self-interest because otherwise you wouldn’t be doing it).

As theorists have noted previously (for example, Margolis, 1981), rationality need not imply selfishness. At some level, this is obvious: consider, for example, a volunteer fire department deciding how best to spend its annual capital improvements budget. But in common discourse, even (or especially?) among economists, the two concepts go together, so much so that psychologists have found that people overly attribute self-interest as a motivation even for their own actions (Miller, 1999).

Voting and vote choice (including related actions such as the decision to gather information in order to make an informed vote) are an interesting example of decisions that are rational in large elections only to the extent that voters are not selfish. This in turn has implications for how people gather and weigh information in deciding their votes.

References

This article is based on the paper, “Voting as a rational choice: why and how people vote to improve the well-being of others,” by Aaron Edlin, Andrew Gelman, and Noah Kaplan, from the journal Rationality and Society, volume 19, pages 293-314, in 2007.

The other references cited, in order of appearance, are:

Highton, Benjamin, and Wolfinger, Raymond (2001). “The political implications of higher turnout.” British Journal of Political Science 31, 179-223.
Nagler, Jonathan, and Leighley, Jan (2007). Who votes now? And does it matter?" Paper presented at the annual meeting of the Midwest Political Science Association, April 12, 2007.
Riker, W. H., and Ordeshook, P. C. (1968). A theory of the calculus of voting. American Political Science Review 62, 25-42.
Fiorina, Morris (1990). Information and rationality in elections. In Information and Democratic Processes, ed. J. Ferejohn and J. Kuklinski. University of Illinois Press.
Green, Donald, and Shapiro, Ian (1994). Pathologies of Rational Choice Theory, Chapter 4. Yale University Press.
Gelman, Andrew, King, Gary, and Boscardin, W. John (1998). Estimating the probability of events that have never occurred: when is your vote decisive? Journal of the American Statistical Association 93, 1-9.
Gelman, Andrew, Katz, Jonathan, and Bafumi, Joseph (2004). Standard voting power indexes don't work: an empirical analysis. British Journal of Political Science.
Mulligan, Casey B., and Hunter, C. G. (2003). The empirical frequency of a pivotal vote. Public Choice 116, 31-54.
Caplan, Bryan (2007). The Myth of the Rational Voter. Princeton University Press.
Fowler, James H. (2006). Altruism and turnout. Journal of Politics 68, 674-683.
Fowler, James H., and Kam, Cindy D. (2006). Patience as a political virtue: delayed gratification and turnout. Political Behavior 28, 113-128.
Margolis, Howard (1981). A new model of rational choice. Ethics 91, 265-279.
Miller, Dale T. (1999). The norm of self-interest. American Psychologist 54, 1053-1060.

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Topics:  Politics and economics

Tags:  elections, rational voting

Comments

Your article on the motivations behind 'rational' voting decisions was an interesting read. My concern is that the cost-benefit framework behind RCT is over-extended when applied to voting decisions. True, most rational humans maximize net benefits even if those benefits tend to be altruistic and involve a larger group. Yet, voting decisions are far more complex than any 'RCT author' would care to admit. For example, all parents have a large WTP for their children. Their welfare is one of the more important, if not most important determinant of choices at the ballot box. Here, the altruism camouflages selfishness and extends not across space, but across time, ie, voters vote for the good of the future generation and implicitly, the future of the nation. (The corollary is that voter turnout would probably increase if party platforms delved more in to the welfare of the future generation). The other point is that the frequency and structure of elections, and the particular decision rule applied to determine winners could affect turnout and even choices. Too frequent elections - a common trait of coalition governments in Europe - also negatively affect voter turnout.

Whether illiterates in a developing nation or citizens of a developed nation, voters' decisions are confounded by many factors - self-serving coalitions, funding by lobbyists, the likelihood that the chosen candidate/party would win, credibility of party platforms and uncertainty of candidate positions on future issues, expectations of coalition instability, availability of credible alternatives, corruption and coercion and so on. I doubt voters have either the inclination or the capacity to process this much information and uncertainty in to their voting decisions.

If RCT has a nice ring, so does 'bounded rationality'!

Professor in the Departments of Statistics and Political Science, Columbia University

Assistant Professor in the Department of Political Science, University of Houston