Is Voting Rational?

If you care about other people, it may be rational to vote:

Voting as a rational decision, by Andrew Gelman and Noah Kaplan, Vox EU: 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.

Two questions. The first question is of no importance, just curious which author is "I". Second, suppose that I have the well-being of the community I live in or of the U.S. as a whole as an argument of my utility function (or some measure of community or national  well-being that accords with my preferences). If helping other people makes me happy, why would caring about other people be contrary to my own self-interest? This is essentially a question about the meaning of the term selfish. I assume selfishness means maximizing my utility, which may or may not include the happiness of other people as an argument.

Update: Here is Andrew's response to my comment, and my reply to Andrew.

Comments

[Patricia Shannon]

Is having children rational?
Is falling in love rational?

[Bruce Wilder]

The term, "rationality" has to be remarkably elastic and capacious, and strangely antisocial, for this kind of debate to even take place.

In the midst of a political campaign, I would think it rather obvious that major efforts are expended to organize voting as concerted social action, to persuade people to identify with a candidate or Party, and to vote accordingly.

I don't happen to think voting is a solitary activity. I don't think that the ratiocination behind rationality is solitary, either. Thinking is a social activity -- people think in groups. And, they vote as members of groups.

Back to the drawing board on this one.

[Cynthia]

Gelman and Kaplan write,

"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."

Don't let GOPers get wind of this, otherwise they'll use every trick in the book to make sure nonvoters never vote!

[Patricia Shannon]

Cynthia, you are surely right, since the Repubs have tried to discourage voters in predominantly Demo districts from voting.

[Tom W]

It appears that the philosophical confusion surrounding the word "rational" arises from economists occasionally applying the word "rational" to desires, like self-interest, rather than to the means of achieving them. I think that economists are making a mistake when they speak of self-interest as if it were rational. What is rational (or can be) is the means of achieving a desire, whatever it is; whereas every desire itself is irrational. In other words, there is no _reason_ to want (or not to want) any thing. Not even the desire to live is rational, because it cannot be shown from logic alone that living is preferable to not living.

With that in mind, altruistic behavior can be as rational as any other. Furthermore, malicious behavior could also be rational, even pure malicious behavior with no intent to benefit oneself from it. In fact I think that the existence of pure malicious behavior is a better refutation of the assumption of universal self-interest, because pure malicious behavior is obviously not self-interested and obviously not done with the intent of "secret self-interest" like appearing to be a good person.

Once we have separated rationality from desires and applied it only to its proper sphere--the means of achieving desires--then the confusion surrounding this subject dissipates. Voting clearly can be rational, because it can be a rational means of benefiting the well-being of others, which is a desire not fundamentally different from self-interest or any other desire.

[Patricia Shannon]

Tom, there is much truth to what you say. But it seems to me that the desires to feel good and to be free of discomfort are rational. Or maybe "desire" is not the right word here. "Drive" might be more accurate.

[outsider]

Biologically, bird parents give 50% food to their young. Aunts and Uncles mot similarly ocupied give 25%. Cousins 1/2 that and so on. (source a study in New Zealand I, unfortunately can't properly document)

The biological imperative is to put your closest DNA through time...an informal football game in the Army I witnessed, a white and black opponent got into a quarrel. Blacks and Whites immediately formed two packs to await the outcome, joining their own, independent of the designated "teams".

4000 + American dead...brown skinned bearded others? who cares? Not my DNA. They have oil we need.

Economic "rationality vs. altruism" is a meaningless argument. Perhaps, "they need to sell their resources to survive, and we need to trade for them to survive" would be a more productive starting point.

p.s. See Gen. Odom's address to the Congress

[2slugbaits]

But it feels so good to vote against idiotic politicians. In fact, it feels so good that sometimes I wish I was back in Chicago so I could vote again and again.

[Noni Mausa]

Nice one, Tom W.

I vote in a rather ceremonial manner, like going to church. It's my one instant for putting my hand on the tiller, and I consider it a solemn duty.

Then afterwards I slope off to treat myself to a nice breakfast or lunch.

Noni

[btgraff]

Australia has mandatory voting - an excellent idea as long as the law provides for people to show up and obstain, refuse th eballot or opt out - essentially, we have rights, but with rights come responsibilities (serving in the military, in many countries) - requiring that someone show up at a designated place every to years is hardly onerous.

but right now, how about getting voter registration rules straightened out, and voting machines, or laws that deny the vote to felons (what ever happened to "no taxation without representation - felons pay taxes once out of jail - shouldn't they have some say?)

[Andrew]

btgraff- Disenfranchisement (and not just voting) of criminals is an enormous contributor to the high recidivism rate in the US. 'Only' about 32% of prisoners return to prison within two years in AU, compared to 52% in the US. I could go on and on about the American criminal justice system, but I don't wish to stray too far afield.

Bruce Wilder and Tom W, thanks for the excellent insight.

[Philip]

Boy, talk about much ado about nothing. Obviously the probability of one's vote changing the outcome of a national election are infinitesmal. This is so obvious I have to think just about everyone realizes it. People vote for emotional reasons: a sense of civic duty; wanting to feel part of a candidate's victory (or the other's defeat); to feel an expression of protest; so they can tell others they voted if asked or offer themselves as a good example of citizenship; etc.

It's not rocket science.

says...

Mark Thoma,

You still have Vox Baby on your blogroll. Andrew Samwick is now blogging at http://www.capitalgainsandgames.com/ instead (although I think Vox Baby will remain intact for reference)

[hari]

One may become a devils advocate, and declare that US so-called democracy is NOT really *democratic* because of the level of participation by theoretically qualified electorate. Why? Is it a result of disatisfcation with organized political parties? Or is it an expression of social alienation by a *class* who don't trust the *rulers*?

On the EU continent, level of participation is relatively high compared to US. In some cases, the ratio can climb upto 60-70% or more of eligible voters! There must be some rational reason for such high level of participation; or what do you think?

May be voting should be made *mandatory* and thus involve the masses into participation. The Aussies are a bunch of *individualists* - yet they accept voting as a mandatory law. Look at how they got rid of the exuberance of the GWB *loyalists* at their last general election? They chose a young and dynamic ex-diplomat Labour Leader for PM.

So, there is still hope for America, me thinks.

[Gil]

Is there a hidden 'duh' factor behind people refusing to vote yet complain when elections don't turn out the way they want? Perhaps the greatest humour behind those who refuse to vote is that they make the votes of those who do vote more valuable. (In other words, your vote versus 10,000 voters compared with your vote versus 1,000,000 voters . . .)

[donna]

Being selfish is not rational. Caring about others increases their concern for you, and improves your life.

Selfishness is not a good strategy for anyone. Why more people don't get that, I don't know.

[jean]

Oh, I don't know, Prop 13 in CA was pretty selfish. It knocked the socks off the education system.

[Roland Martinez]

Sending a candidate to office in a landslide is a message as well though.

Let's say that your candidate is going to win the election, voting regardless does two things:

1. It puts the candidate that you are casting your vote for on notice that you're paying attention and that they had better do what they said they were going to do while they were campaigning.

2. It's a warning to their opponents and future candidates that if they don't go along with what you voted for that they will be losing their job next. Think of what agenda senators who are up for relection in two years and the house of representatives will be persuing if any single presidential candidate wins by a 10% margin.

Stupid economists. Send that man back to Econ 201 to review signaling again. The signaling benefit is worth more to politicians and the people who vote than the chance of the vote being decisive and I didn't need any greek letters to come to that conclusion.

[Patricia Shannon]

donna

You are so right. The way we treat others helps to create the kind of world we live in.

I would fine-tune the golden rule, though. Continuing to help those who are habitually selfish is counter productive. It teaches them that their way is acceptable.

I have come to the conclusion that to improve society, we should focus our helping on the kind of people who are themselves helpful. I have to admit, being softhearted, I don't always follow that, but I do much more than when I was younger.

[Patricia Shannon]

I read a study that examined the relationship of several psychological characteristics of people from poor families, and whether they were related to the probability that the person moved up at least one (maybe it was two) economic classes when they were grown. They found 3 of the characteristics were associated with moving up from the bottom class. One was intellectualization, which does not surprise me. Another was empathy. People who had empathy helped others, which caused others to help them. (I can't remember the 3rd factor).