Why it can be rational to vote

by Andrew Gelman on November 1, 2010 · 5 comments

in Campaigns and elections

I think I can best do my civic duty by running this one every Election Day, just like Art Buchwald on Thanksgiving. . . .

With a national election coming up, and with the publicity at its maximum, now is a good time to ask, is it rational for you to vote? And, by extension, wass it worth your while to pay attention to whatever the candidates and party leaders have been saying for the year or so? With a chance of casting a decisive vote that is comparable to the chance of winning the lottery, what is the gain from being a good citizen and casting your vote?

The short answer is, quite a lot. First the bad news. With 100 million voters, your chance that your vote will be decisive—even if the national election is predicted to be reasonably close—is, at best, 1 in a million in a battleground district and much less in a noncompetitive district such as where I live. (The calculation is based on the chance that your district’s vote will be exactly tied, along with the chance that your district’s electoral vote is necessary for one party or the other to take control of a house of congress. Both these conditions are necessary for your vote to be decisive.) So voting doesn’t seem like such a good investment.

But here’s the good news. If your vote is decisive, it will make a difference for 300 million people. If you think your preferred candidate could bring the equivalent of a $50 improvement in the quality of life to the average American—not an implausible hope, given the size of the Federal budget and the impact of decisions in foreign policy, health, the courts, and other areas—you’re now buying a $1.5 billion 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 the country as a whole, rather than their personal betterment. Indeed, when it comes to voting, it is irrational to be selfish, but if you care how others are affected, it’s a smart calculation to cast your ballot, because the returns to voting are so high for everyone if you are decisive. Voting and vote choice (including related actions such as the decision to gather information in order to make an informed vote) are rational in large elections only to the extent that voters are not selfish.

That’s also the reason for contributing 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.

The social benefit from voting also explains the 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: for example, as one of 1000 respondents to a Gallup 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 to estimate how often individuals are surveyed (the answer was about once per year). It is thus unlikely that a response to a single survey will have much impact.

So, yes, if you are in a district or state that might be close, it is rational to vote.

For further details, see our articles in Rationality and Society and The Economist’s Voice.

I’d like to add one more thing. You’ve all heard about low voter turnout in America, but, among well-educated, older white people, turnout is around 90% in presidential elections. Some economists treat this as a source of amusement—and, sure, I’d be the first to admit that well-educated, older white people have done a lot of damage to this country—but it’s a funny thing . . . Usually economists tend not to question the actions of this particular demographic. I’m not saying that the high turnout of these people (e.g., me) is evidence that voting is rational. But I would hope that it would cause some economists to think twice before characterizing voting as irrational or laughable.

(And, no, it’s not true that “the closer an election is, the more likely that its outcome will be taken out of the voters’ hands.” See the appendix on the last page of this article for a full explanation, with calculus!)


Ricketson November 1, 2010 at 8:59 pm

“If you think your preferred candidate could bring the equivalent of a $50 improvement in the quality of life to the average American”

This assumption seems quite arrogant given that half of the country seems to disagree with you. I can think of only two ways to interpret the fact that the voters are roughly evenly split:

1) There are two factions, and one will win while the other will lose. One will gain $50 per person, while the other will lose $50 per person. Voters believe that they are promoting the general welfare, but their perception of the general welfare is biased by their own experience, and their limited social circle.

2) There is essentially no difference between the candidates. At least, a voter has no ability to judge the costs and benefits of the two candidates (who are strangers to the voter). The candidates/leaders have already been vetted by the political establishment, and are not substantially different from each other (they may be different in their policy preferences, but the pluses and minuses balance out).

Andrew Gelman November 1, 2010 at 9:06 pm


You can call it arrogant if you like, but the election is important to millions of people. Personally, I think it’s arrogant to tell people that their vote doesn’t matter.

To get to your questions:

1. No. Policy is not a zero-sum game. Suppose you’re Paul Krugman. You believe that if the D’s control the government, they can bring the economy back to life, whereas if the R’s come to power, they’ll keep us in a depression. (Or, similarly, from the other perspective.) The $50 per person does not represent $50 worth of joy that your party wins, it represents an average $50 of happiness for everyone because of the near-universal benefits of peace and prosperity.

2. Of course, there are big differences between the candidates. Nolan McCarty and many other political scientists have done extensive research on the differences between the two parties. D’s and R’s have big differences on a lot of issues, from abortion to military policy to taxation.

Yokel November 2, 2010 at 4:18 pm

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: for example, as one of 1000 respondents to a Gallup 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%).

Now hold on just a second. If the justification for voting is that a person might, however improbable it is, determine policy outcomes by deciding an election with a single vote, when would responding to a poll ever be rational? Unless you’re arguing that there’s an intrinsic benefit to deciding for its own sake. In which case I’ll stay home today, making decisions (sausage or pepperoni?) over which I have complete control.

ricketson November 2, 2010 at 5:45 pm

(if I have submitted this twice, it is because I got an error on my first attempt. I previewed and then posted, and it didn’t go through. This is the same thing that happened with my earlier comment. It may be because my browser does not have Javascript.)

The first sentence of my previous comment is poorly written. This probably made my point hard to understand and made it seem more confrontational than I had meant it to be. I’m sorry about that; I thought I had fixed it while previewing.

I did not mean that half of the voters disagreed with “you” (Andrew Gelman), I meant that half of the voters disagree with the hypothetical voter who is stepping into the booth during a close election. In that scenario, I think it is arrogant for the voter to think to himself “my decision is going to make this country a much better place” even though half of the people in the country apparently believe that it will make the country a much WORSE place.

How can we decide if Americans will benefit from the win of one party over the other? Well, we could ask each American if they and the people that they know will be better off following the victory of a particular party. The best survey that I have access to is the election itself, and based on that survey, it seems that roughly equal numbers would benefit or lose from any outcome (or else the outcome is so certain that my vote has no chance of changing things).

Finally, for every Krugman there is also a Beck. I happen to agree with the Dems on some issues, and the Reps on other issues. Apparently, a large number of voters feel the same way based on how many are undecided on election day. So the Democrats get a +$50 for their position on abortion, and the Republicans get +$50 for their position on international trade. Even though their positions are very different, the net value of these differences is zero.

ricketson November 2, 2010 at 10:26 pm

I just read a chunk of the “rationality and society” article (the first 13 pages), and it helps to clarify the issues here.

First, following up on Yokel’s comment, it would be interesting to see if there are other reasons to vote aside from the potential to affect the election. Do votes for a losing candidate encourage him to run again? Do these votes win publicity for the causes of the losing candidate? Do they increase the chance that the winning candidate/party will adopt part of the platform of the loser?

Does voting itself (regardless of for whom the vote is cast) affect policy? For instance, does it help to protect political rights/freedoms (use it or lose it)?

The social-benefit model of voting behavior looks powerful. It is also consistent with my own experience of how people speak about voting.

As I’ve been harping on above, I wonder what goes into the variable “B” (total social benefit). The paper makes the case that many voters expect their favored candidate to deliver a large social benefit; however, it does not examine whether they are correct in this estimate. In fact, this model suggests that many voters are completely wrong in their estimate of B (i.e. they are favoring the wrong candidate).

The question that has been bugging me is how do we reconcile that inference with this blog post’s suggestion that voting is worthwhile BECAUSE of the large benefit that we expect.

If we expect our favored candidate to deliver a large benefit, are we deluding ourselves? Assuming that we are no smarter or better informed than other voters, it seems that we have a 50% chance of voting for the right candidate and 50% chance of voting for the wrong candidate. In that scenario, the expected benefit from tipping the election should be roughly 0, since we have low confidence in our own decision.

There is a fundamental difference between saying that it is rational to vote (given a perception of the benefit of tipping the election) and saying that it is worth our while to vote (given uncertainty about our own judgment).

One way to reconcile this is to say that voters are not trying to estimate the total effect of electing one candidate over another; they may be evaluating a specific part of the difference and relying on the election itself to average across the population (or integrate the individual analyses into a single welfare-maximizing decision). For instance, the voter may be casting his vote based on a single issue, or the welfare of a specific constituency. If this is accurate, then two voters can support different candidates and both have correct estimates of which candidate is better (with regards to their specific interest).

One problem with this theory is that it is not consistent with how people talk about politics (they tend to advocate for parties or candidates as total packages). However, it is possible that political speech is biased towards those who are committed to candidates or parties, and not single issues or sub-constituencies.

Comments on this entry are closed.

Previous post:

Next post: