Why it's (often) rational to vote:

The upcoming election raises the important question of whether it's rational for you to vote. You might think that the answer is obviously "yes." But economists and other rational choice theorists have long argued that voting is irrational. Why? Because there is only an infinitesmally small chance that your vote will make a difference. In a U.S. presidential election, the chance that one vote will decide the outcome is less than 1 in 100 million, and it is still extremely small even in elections for the House or Senate. Thus, the 30 or 40 minutes of time that it takes to vote is probably far more valuable than whatever benefit you hope to derive from the "right" candidate winning, if the latter is divided by the ludicrously tiny chance that your vote will be decisive.

Critics of rational choice theory, of course, have had a field day arguing that rational explanations of human behavior are invalidated by the obvious fact that millions of people do vote, despite its being irrational to do so. The critics are, quite rightly, not swayed by arguments that voting is rational because people feel they have a "duty" to go to the polls. After all, why would it be rational believe you have a duty to do something that makes no difference? Duty-based explanations don't rescue rational choice theories of voting; they just add another layer of irrationality to the mix.

In fact, however, both sides are wrong. It is indeed rational for many people to vote, and therefore the existence of widespread voting is not evidence against the validity of economics or rational choice theory. For a detailed explanation, complete with equations, see my forthcoming article here.

The key insight is that the traditional rational choice theory of voting implicitly assumes that the voter cares only about their own self-interest, narrowly defined. But if you care even slightly about the potential benefits to fellow citizens of ensuring that the "right" candidate wins, then the sum total of those benefits might well outweigh the (generally low) costs of voting even after discounting for the fact that there is only a minute chance that your vote will make a difference. Real-world voters, of course, probably don't go through detailed calculations of the sort that I describe in the article. But they do likely realize that their is little chance that their vote will make a decisive difference, while also caring at least slightly about the welfare of their fellow citizens. And the combination of these two assumptions is enough, for many people, to make a rational decision to vote.

Of course, under these assumptions, it will be rational to vote only if you perceive a significant difference between the two opposing candidates or parties. And, as I note in the paper, studies do indeed show that those who perceive a big difference between the two sides are far more likely to vote than those who don't.

This theory is not entirely original to me; it was in fact proposed by philosopher Derek Parfit in his 1984 book Reasons and Persons (pp. 73-75); what I have done is explore its implications for voting theory more generally. Until now, Parfit's theory has been largely ignored by academic scholars of voting, perhaps because Parfit is not an economist or political scientist, and his book is primarily devoted to other subjects.

Not all the implications of the Parfit model are reassuring. As I show in my article, despite the fact that it is rational to vote, it is also rational for most people to be poorly informed about politics (primarily because acquiring and processing political information is much more costly and time-consuming than voting). For the minority that is well-informed, it may well be rational to analyze the information they do have in a biased and illogical way. Thus, a rational population is likely to have a large number of people who choose to vote but also tend to be ignorant and/or illogical about politics.

UPDATE: Some commenters argue that it's rational to vote because of the chance that, even if your vote isn't decisive, it can send a "message" about the degree of support for a particular candidate, policy, or party. But the same logic applies here. The chance that the "message" will be "received" is only infinitesmally greater if Candidate X gets 10 million votes than if he gets 9,999,999. The impact of any one vote on the probability of successfully sending a message is unlikely to be much greater than its impact on the probability of winning the election.

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Voting and the Wisdom of Crowds:

Several commenters on my post on the rationality of voting brought up James Surowiecki's interesting book, The Wisdom of Crowds. It so happens that I wrote a review of the Wisdom of Crowds last year, where I explained why his argument that large numbers of individually ignorant decision-makers can make seeemingly well-informed collective choices does not work well in the context of voting. For those interested, the review is available here.

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The Possible Rationality of Voting; Another View.--

My co-blogger and former (visiting) colleague Ilya Somin has an interesting article on the rationality of voter ignorance forthcoming in Critical Review, which he blogged about yesterday. On empirical matters, Ilya and I usually agree, often using some of the same data sources to make our points. But here, we seem to differ on a theoretical matter based on a difference in modeling assumptions.

In his post, Ilya argues that, because of altruism, voting is rational in order to increase the probability that your preferred candidate will win. As I will explain below, I think that one can come up with a story consistent with rational voting, but probably not the story that Ilya tells.

Ilya summarizes his argument in his post:

The key insight is that the traditional rational choice theory of voting implicitly assumes that the voter cares only about their own self-interest, narrowly defined. But if you care even slightly about the potential benefits to fellow citizens of ensuring that the "right" candidate wins, then the sum total of those benefits might well outweigh the (generally low) costs of voting even after discounting for the fact that there is only a minute chance that your vote will make a difference. . . .

This theory is not entirely original to me; it was in fact proposed by philosopher Derek Parfit in his 1984 book Reasons and Persons (pp. 73-75); what I have done is explore its implications for voting theory more generally. Until now, Parfit's theory has been largely ignored by academic scholars of voting, perhaps because Parfit is not an economist or political scientist, and his book is primarily devoted to other subjects.

Of course, perhaps the other reason that Parfit's theory has been largely ignored is that it is appears to be wrong.

Ilya's Equation

In doing his modeling and making what he says are "plausible assumptions," Ilya assumes that the odds of casting the deciding vote are 100 million to 1 and that people value their own utility 1000 times more than each other individual's utility.

The equation on the rationality of voting that Ilya refers to is this (Somin manuscript, page 4):

(((Expected Difference in Welfare per person if the preferred candidate wins) x (300 million people) / 1000) / 100 million)) - Cost of Voting = Expected Utility of Voting

Ilya assumes that the cost of voting is $10, and the expected benefit per person of the preferred candidate winning is $5,000. If you plug in these numbers, the result is:

($5000 x 300,000,000 / 1000) / 100,000,000) -- $10 = $5 (net expected value of voting).

Accordingly, Ilya concludes that voting would be rational because the expected benefit of $15 is larger than the expected cost of $10, leaving a net expected benefit of $5 for voting.

A Serious Problem With One Assumption

One of the nice things about equations is that their assumptions are usually explicit. Look more closely at Ilya's equation and what it says about voter preferences BEFORE the 1 in a 100 million discount is applied.

Ilya's equation assumes that, if a voter could guarantee a victory for his preferred candidate, a typical voter would be willing to pay only $5,000 for one person's benefit (presumably his own), but that the same voter would be willing to pay about $1.5 billion dollars to benefit others ($5,000 x 300 million people / 1000). In other words, Ilya assumes that a rational voter when voting values the total utility of other Americans 300,000 times more than he values his own total non-altruistic utility ($1.5 billion to $5,000). Moreover, even leaving aside the comparative valuation, it can't be that (because of altruism) the utility to each person voting of having one's preferred candidate certain to win would be $1.5 billion dollars. To say that these are extraordinarily implausible assumptions is an understatement.

I think, for example, that if most individuals were given a choice between half a billion dollars for one's own bank account and certain victory for one's preferred presidential candidate, most individuals would be willing to switch allegiances and take the half billion dollars. Indeed, I suspect that a majority of individual voter's allegiances could be purchased for a secret political consulting job paying much less than $200,000 per person (assuming certain victory for the candidate doing the hiring).

So let's make a much more rational assumption, but still one that is unrealistically generous to Ilya's position. Let's assume that a typical voter has a family gross income of $50,000 and a take-home pay of $35,000, and like Ilya, let's assume that the voter would be willing to pay $5,000 just for one person's benefit (his own) to guarantee a win for his preferred presidential candidate. Now let's be extraordinarily generous to Ilya's position and assume that the typical voter is highly altruistic and would be willing to pay another $35,000 (an entire year of his family's take-home pay) just to benefit others, not himself, by having his preferred candidate win.

Plugging this into Ilya's analysis, the expected benefit to each person of voting would be $40,000, divided by 100 million (the probability of casting the deciding vote), which is only 4 one-hundredths of a penny. Obviously, voting would be highly irrational, since the expected benefit to even a highly altruistic voter of just 0.04 cents is much less than Ilya's assumed cost of $10 for voting. Thus, even for an extraordinarily altruistic voter, voting is highly irrational if its purpose is to influence the outcome of a presidential election.

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More on the Rationality of Voting - Reply to Jim Lindgren:

Co-blogger Jim Lindgren has a thoughtful response to my analysis of the rationality of voting. To briefly recap, I argue that voting is rational if 1) voters value the utility of their fellow citizens as well as their own, and 2) they perceive a big enough difference between the "right" candidate and his or her opponent. In reply, Jim makes the point that I may overestimate the extent to which people value the utility of others relative to their own. I assumed, in my analysis, that they value benefits to fellow citizens on average, 1/1000 as much as they value benefits to themselves. Jim argues, however, that:

Ilya's equation assumes that, if a voter could guarantee a victory for his preferred candidate, a typical voter would be willing to pay only $5,000 for one person's benefit (presumably his own), but that the same voter would be willing to pay about $1.5 billion dollars to benefit others ($5,000 x 300 million people / 1000). In other words, Ilya assumes that a rational voter when voting values the total utility of other Americans 300,000 times more than he values his own total non-altruistic utility ($1.5 billion to $5,000). Moreover, even leaving aside the comparative valuation, it can't be that (because of altruism) the utility to each person voting of having one's preferred candidate certain to win would be $1.5 billion dollars. To say that these are extraordinarily implausible assumptions is an understatement.

I have two responses to Jim's point, one technical, the other intuitive. Let's take the intuitive point first: Jim's analysis assumes that the relationship between the amount of money you are willing to give up to benefit others and the amount of benefit they receive from the sacrifice is purely linear. That is, if you are willing to give up $1 so that your neighbor will get $1000, you are also willing to give up $1.5 billion in order to give your fellow Americans $1.5 trillion. To my mind, the second doesn't necessarily follow from the first. Jim has shown that my analysis becomes implausible in cases where the voter/citizen is called upon to make very large sacrifices. When we're talking about voting, we're generally talking about a very small sacrifice.

Second, the technical point. Jim has (understandably) conflated the distinction between dollar income and utility. My analysis assumes that people value the utility of others at 1/1000 of their own, which is not the same thing as valuing the added dollar income of others at 1/1000 of the rate at which you value adding dollars to your income. When we're talking about making a sacrifice of $35,000 out of a $50,000 annual income (to use Jim's example), we're talking about a vastly greater loss of utility to the donor than when we're talking about sacrificing $10. And the difference between the two may well be much greater than $35,000/10. The $10 sacrifice is essentially trivial, while the $35,000 may wreck the donor's life for months or years to to come.

The slightly altruistic donor/voter of my model might well reason that this massive sacrifice on his part outweighs the utility gain to the rest of the population from having the right candidate win, so long as he discounts the latter by a factor of 1000. It's worth noting, however, that there are in fact people who sacrifice the equivalent of 70% of one year's income to try to ensure that their preferred candidate will win an election. Many campaign volunteers do precisely that. I suspect that there would be more such people if they could be assured that their sacrifice would guarantee victory, rather than just increase the likelihood somewhat at the margin.

In a large and diverse electorate, the 1/1000 figure is best viewed as a rough average rather than as a precise estimate of every individual voter's degree of altruism. In reality, some people are much less altruistic than this and others more so.

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Civic duty and "pleasure" as explanations for voting:

Both Jim Lindgren and many commenters on our earlier posts on voting suggest that the real explanation for why people vote is that they they feel they have a duty to do so. This is the standard explanation for voting in the academic literature and it makes intuitive sense. If you ask people why they voted, most will indeed probably say that it was because they had a civic duty to do so.

However, the question remains, why would people think they have a duty to do something that makes no difference? We don't normally believe in a duty to do futile acts. The reason why people feel they have a duty to vote is because they tend to believe that voting makes a "difference," even if a very small one. If they thought otherwise, very few would still believe they had a duty to vote. To be sure, an alternative explanation is that they think they have a duty to vote because they have been indoctrinated into believing this by the government, particularly in the public schools. While that may be true to some extent, mass voting long predates large-scale indoctrination of this kind, and indeed long predates the existence of public schools (which were not established in most of the United States until the mid to late nineteenth century). Moreover, it would be hard to understand why this kind of indoctrination is so much more successful than other such efforts in relatively free societies.

The same point applies to arguments that people vote because they get "pleasure" from it. I highly doubt that many people enjoy the actual process of voting, which mainly consists of standing in line and then filling out a form. For that reason, I am skeptical about Jim's suggestion that the benefit voters get from casting a ballot is "like going to a movie or a football game." Movies and football games are entertaining and fun (at least to fans). Voting is not. Very few people regularly choose to stand in line or fill out forms as a leisure activity. The real "pleasure" that people get from voting (to the extent that they get any) is the sense that they have done their duty. But this in turn merely gets us back to the question of why they think they have such a duty in the first place.

UPDATE: In response to this post, Orin Kerr writes:

When an event is far away, we tend to ignore the practical consequences of it and instead latch on to a very incomplete vision of what the event may be like. So if a co-worker says, "do you want to go to Vegas with me 6 months from now?," you might be happy to accept because the abstract mental image of going to Vegas seems great. It's not until the trip is around the corner that you realize that the trip will be expensive, you have other things to do, you don't necessarily want to spend time with your co-worker, and the like.

Applying this idea to voting, it suggests to me that Jim may be right about why people vote even if Ilya is right that people don't like to wait in line and fill out forms. When people think about voting in the abstract, they focus on the rush of it; the feeling of participating, of taking responsibility, and the excitement of not knowing who is going to win. Sure, they don't like to wait in line and fill out forms. But when they decide to vote they aren't thinking about that, just like they aren't thinking about what a pain it is to go to Vegas when the trip is six months away

The problem with Orin's argument is that, unlike the trip to Vegas, the decision to vote can easily be reversed, even at the last minute. There are no nonrefundable airline tickets, hotel reservations, etc. Therefore, even if it is true that, in thinking about a decision months ahead of time, people don't focus on the costs (which I'm skeptical about), they surely do realize the costs by the time election day comes around. Moreover, I highly doubt that most people even think about the decision whether or not to vote many months in advance.

UPDATE #2: Frank Cross, one of the commenters to Orin's post writes:

I think the comparison to voting for all stars, or American Idol, or other polls is suggestive.

Ilya's theory doesn't apply well in these cases, I don't think the selection of a player to the all star game will yield benefit for many other Americans, and I don't think my single vote for the player will likely make a difference in the outcome.

On American Idol, people can vote simply by calling in on a toll-free line while watching the show. There is therefore virtually no cost to doing so; assuming you would be watching the show during that time period anyway, the only possible "cost" is the diversion of part of your attention way from the TV screen for 30 seconds or so. If you had to take an hour to go to a polling place to vote on AI, I think very few people would do so (even those who like the show). The fact that the producers have created a toll-free line for callers suggest that they realize that the voters are unwilling to pay even a very small cost to participate (a 1 minute long distance call probably costs no more than 10 or 15 cents).

Voting for sports all-stars is a very different phenomenon from political voting. The people who fill out all star ballots generally have a strong interest in the sport in question and actually enjoy the process of thinking about which players should get in and which ones shouldn't. All-Star ballot voters are a small minority of the public, probably even of sports fans. Moreover, all star game voters can legally "stuff the ballot" by voting many times, which greatly increases the chance of affecting the outcome. Casting several hundred or even several thousand votes for your favorite player is a much stronger incentive to vote than being able to cast just one. Major League Baseball deliberately encourages ballot-stuffing because they know it increases "turnout" and interest in All Star game elections.

A small minority of people are "political fans" and feel the same way about politics as sports fans do about sports. But the vast majority of people who vote do not in fact have this kind of strong interest in politics, and of course stuffing the ballot in a political election can land you in jail!

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