Voting is Rational After All

One of the hobbyhorses of the rational-choice economics types is that voting is irrational. The odds of your vote making a difference are ludicrously small, so why bother?

Readers may recall that the New York Times picked up on the argument by Lloyd Cohen of George Mason Univerisity that, contrary to widely held views, buying a lottery ticket is not irrational. The problem is that most analysts saw the payoff as the likelihood of winning, which is indeed ludicrously small. But Cohen argued that that view missed the main motivation completely. The real point is fantasizing about what one would do with the winnings, which you can’t do meaningfully with no skin in the game. Thus, playing lotto is a consumer disposable, similar to buying a lifestyle magazine.

Andrew Gelman and Noah Kaplane compare define the outcomes differently than most rational choice economists, who focus on personal benefits Just as in lotteries, the likelihood of your vote swinging an election is pathetically small. But the payoff is vast. Just imagine the costs (and lives) that would have been saved if Gore had won and America’s Iraq misadventure has never come to pass. Differences among policies by major candidates often total tens of billions, if not hundreds of billions, of expenditures. which even divided by large numbers of voters, still equates to a large potential payoff per act of voting.

From Vox EU:

Voting behaviour seemingly confounds rational choice theory. But this column shows that voting can be perfectly rational, if voters are concerned with social benefits and not merely personal gains. Rationality and selfishness are not the same.

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).

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.

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.

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  1. Steve

    I’m in favor of any argument that might get people to vote, but the authors’ interpretation of the probability term in the utility function is a little problematic. If you vote and your candidate wins by one vote, you can’t conclude that your vote was decisive. Every vote for that candidate was decisive. If you don’t vote but do prefer a candidate, and that candidate loses by one vote, your failure to vote wasn’t decisive either, unless you were the only non-voter in the population who preferred the losing candidate. No one can point to the single voter or non-voter who won the lottery of `making all the difference.’

  2. Yves Smith


    Agreed. For what it’s worth, I’ve never been a fan of rational choice economics. The literature on cognitive biases is too deep for it to hold true. And people can often have legitimate and conflicting motivations which don’t fit neatly into that paradigm.

  3. Steve

    Yeah it’s interesting if you go back to F.P. Ramsey, you see him discard a number of claims later made by rational choice theorists who adopted his partial beliefs framework of subjective probability (many economists probably don’t even know who Ramsey was). He didn’t claim that people couldn’t be inconsistent in their beliefs, only that inconsistent beliefs can be exploited to another’s gain. He didn’t claim that people learn from their mistakes. Most of all, he never claimed that a consistent set of beliefs was eo ipso reasonable. It’s pretty funny that rational choice theory imposed itself as an ideology just at the time that mass advertising came along to exploit irrational consumer behavior.

  4. Anonymous

    What’s much more rational is to use your consumption behavior to influence electoral outcomes: the Fair model makes economic factors uniquely important in the aggregate, and to the extent that your consumption has a multiplier effect, it influences others with or without their concurrence. This is a vote that can’t be negated by caging or electoral fraud. And you can express the strength of your conviction by being more or less of a skinflint.

  5. Dave Raithel

    RE Steve and Yves: Several points:

    1) This becomes a dispute between counterfactuals and facts – “coulda-shoulda-woulda, if I’d only known” and “But you didn’t.” Steve’s argument sure seems valid and sound, but the voice in my head replies my not knowing that there was no other non-voter preferring my losting candidate is irrelevant to my responsibility – or failure to act responsibly.

    2) Distinguishing between “reason” and “rationality” seems to eventually run up against values, and the last time I looked, rational choice theory still took values as given – preference orderings have formal properties, but what one values is neither rational nor irrational, per se.

    3) Though neither would I claim to be a fan of “rational choice” economics, it’s a useful heuristic tool, and sometimes a studied application of “false consciousness.” And sometimes, it might explain the facts – perhaps Riker’s model better explains the voting behavior of members of Congress than my or yours…

  6. Anonymous

    P=0, the probability one vote is decisive is zero. The error rate in counting votes results in totals that vary by at least a few hundred votes in successive recounts. Second, if an election has a margin of victory significantly less than 1%, it is the policical equivalent of a jump ball, or a fumble. In the US, the party that lost the first count tries to force as many recounts as possible (hoping that they will eventually win one), and the party that won the first count tries to prevent or limit recounts. This pattern has happened in many congressional elections, and was followed in the Florida fiasco. So, you end up with C-D, and you can ignore the idea of your vote affecting the outcome (it can’t). I think a lot of C comes from people considering the scenario where the candidate you don’t like wins, they can at least say I voted against that (insert expletive)

  7. Anonymous

    I think there’s a very practical benefit that’s being totally ignored. Say you live in a district that typically votes 75% Republican. You know that every Republican candidate from top to bottom is going to win. Nonetheless, you take the time to vote Democratic top to bottom. If enough people are motivated to do the same, Republicans might still win by 60%. But you’ve done more than gained a small measure of personal satisfaction, you’ve sent a very effective message, one that will be heard from the dogcatcher to the Presidental candidate.
    Now it’s still true that your one vote doesn’t really matter unless it’s combined with a bunch of others, but if you believe that a lot of people are fed up and will vote similarly, you’re motivated to vote, turnout is higher and you’ve actually caused a change.

  8. Dave Raithel

    Nothing like considerations on rational choice theory implications to induce a bout of meloncholy.

    On the different Anonymous points: Not that you mean to suggest it, but the reasoning you offer suggests that democracy is futile. Maybe it is; may it would be better to live under benevolent dictatorship punctuated by violent changes for dictator. (From here we could reflect on just what, exactly, Arrow’s Theorem tells us about the processes by which we choose candidates and then office holders.)

    A different Anonymous suggests that even futile voting sends messages – but on this, Riker’s other main contribution, I recall, was extending the analyis of Down’s Economic Theory of Democracy to the concept of “the minimal winning coalition” On that analysis, nobody who wins CARES what message you might be sending so long as they win, and that requires just 1 more than half. To hedge, of course, the minimal winning coaltion might be expanded in members. Some data suggests that 4/7 of the vote is a safe place to stay, forever. All this, of course, can be complicated by pointing out, say by citing Frank (What’s the Matter with Kansas?) or others that a lot of the people who think they are part of that winning coalition are just screwing themselves, but this just circles back to my earlier comments of the day ….

  9. Anonymous

    I recommend Bryan Caplan’s book: Myth of the Rational Voter.

    I think it sheds a lot more light on the subject that the work you’ve cited Yves.

  10. Patri Friedman

    No one seems to have mentioned the key point. Yes, this analysis is a reasonable argument that lottery ticket purchases are rational. Yes, it is also a reasonable argument that voting is rational.

    *However* it does not imply that learning anything about the candidates is rational. Thus it does not in the slightest contradict “Rational Ignorance”, which is the more recent version of the rational-choice argument.

    And in fact, your point supports this argument! If the benefit of voting is fantasizing about what would have happened if your candidate won, then people will vote, not based on who will be best for the country, not based on educated research, but on which candidate gives them the best warm fuzzy feeling.

    No wonder we end up with so much demagoguery.

    And I’ll second the recommendation for Bryan Caplan’s book – its argument is much more sophisticated than the strawman you skewer here.

  11. Anonymous

    I found this post interesting and as I read it I thought about why I vote and here are my reasons (demonstrating rationality):

    I want to ensure a candidate or laws that will act wisely and be just.

    If my candidate wins, or if the proposition I vote for passes, then I have helped society and I have done my duty.

    If my candidate loses, or if the proposition I vote for fails to pass, then I have at least done what I could.

    By this rationale, I still get personal satisfaction from voting, whether or not my views actually carry the day.

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