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Yes, it can be rational to vote. Yes, your vote could determine the outcome of the election. Maybe if 90% of well-educated, older white people do something, we shouldn’t be so quick to dismiss it as “irrational.” Etc.

Seeing as the Freakonomics people were kind enough to link to my list of five recommended books, I’ll return the favor and comment on a remark from Levitt, who said:

Nobody in their right mind votes because they think they’re going to affect the outcome of an election. If you look over the last hundred years of, say, elections for the U.S. House of Representatives, I think there’s been maybe one [very close] election that’s been decided by votes. And in the modern era, elections that are close are always decided by the courts. There’s always litigation — look at what happened with Bush against Gore. So in no meaningful way can you say that your vote will ever decide an election. The reasons for voting have to be something very different: it’s fun, your wife will love you more if you do it, it makes you feel like a proud American — but never should anyone delude themselves into thinking that the vote they cast will ever decide an election. … Just about anything you do with your time would be more productive [than voting].

I’ve discussed this before (see also the string of entries here), so this time I’ll keep it brief. Levitt is making a couple of mistakes:

1. At a purely technical level, it’s not true that litigation of elections means that a single vote can’t matter. Most elections are not litigated, and your vote can be the one that makes the election close enough to send it to the courts. Under any reasonable model, the probability that your vote determines the election is the same whether or not the courts are involved, and you can show this by adding up the probability of any vote margin being decisive. For a mathematical derivation, see page 674 of our article in the British Journal of Political Science.

2. We estimate the probability of your vote being decisive in the presidential election as about 1 in a million, at best. (See, for example, our paper in Economic Inquiry.) But–and this is a big “but”–if your vote does swing the election, this could be a big deal. From the voter’s standpoint, a national election is like a lottery: there is a very very small chance that your vote can matter, but if it does, you can get a big payoff. In this case, it’s not a personal payoff; rather, it’s the social payoff of making the world a better place (as you see it). We discuss this in our article, “Voting as a rational choice: why and how people vote to improve the well-being of others,” in Rationality and Society (see also this shorter version published in the Economist’s Voice).

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.

3. Levitt says: “Just about anything you do with your time would be more productive [than voting]”: Define “productive.” Is playing chess productive? Going to the movies? Sledding? Etc.

That said, I agree with Levitt’s point that there are a lot of other reasons for voting besides affecting the election. Levitt, Dubner, and I live in New York and Illinois, where any vote has an extremely low probability of determining the presidential election. (First off, it’s highly unlikely that New York or Illinois will be so close that one vote can make a difference; second, if either of those states is tied, we’re probably in an electoral landslide, in which case swinging either of these states’ vote won’t change the Electoral College winner.) I vote anyway. So I’m certainly not claiming that rational decision making is the only reason or even the most important reason to vote. What I’m saying is that it can be rational to vote. “Rationality” does not have to equal “selfishness.”

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.

P.S. I don’t mind that Levitt doesn’t want to vote, and I’m not saying that it’s rational for everyone or even most people to vote, and it’s fine for Levitt to present arguments against voting, but I don’t think it’s so great for them to him to use his wide influence to spread the notion that “voting doesn’t make good economic sense” as if this is some sort of absolute truth. I think it is far more consistent with the best principles of Freakonomics to try to understand people’s behavior, not to snarkily dismiss it as not making sense.

P.S. Joe Bafumi, Aaron Edlin, Gary King, Noah Kaplan, Jonathan Katz, and Nate Silver participated in various parts of the research discussed above.

30 Comments

  1. Adam says:

    OK, you lost me. How could a single vote ever be decisive? I do not understand the mathematics of it. Even in a very local election where the results were determined by, say, 50 votes, one of those 50 could have decided not to vote and there would still be 49 other people who would have created the same outcome.

  2. Sebastian says:

    I've given up on reading the Freakonomics blog by now, there standards have just gotten shockingly low.

    I looked at the post you link to and he has this bizarre piece of dating advice:

    My advice would be: while you’re waiting to be successful, spend your time in becoming successful and worry about dates once you’re successful because it’ll be so much easier to get dates once you’re successful.

    Jeff Ely has noted before that Levitt is a bad game theorist and this is yet another example: If you find a partner before s/he knows if you're going to be successful, i.e. under a type of veil of ignorance situation, you can be much more confident about his/her motives (which I'd think of as asymmetric information).

    It would also at least be worth considering if you miss the "highest quality" matches if you join the search too late – people have made that argument for the academic job market.

    Point being is that if I ask an economist about dating advice, I'd at least want to hear these considerations, yet Levitt just provides only one rather superficial aspect. (which I guess is supposed to be counter-intuitive).

  3. Brenton says:

    Also, the logic of "no one should vote" doesn't hold up when we think about it in game-theoretic terms. It's obviously not a Nash equilibrium for no one to vote, since then any prospective voter would be pivotal with probability 1. Moreover, game theorists have shown that there are equilibria with high levels of turnout in large elections. See the following papers:

    Palfrey, T., Rosenthal, H. 1983. A strategic calculus of voting. Public Choice 41(1), 7–53.

    Palfrey, T., Rosenthal, H. 1985. Voter participation and strategic uncertainty. American Political Science Review 79(1), 62–78.

    Kalandrakis, T. 2009. Robust rational turnout. Economic Theory 41, 317-343.

    This isn't to dispute Andrew's additional explanations for why voting can be rational from a decision-theoretic point of view — just to say that voting is even more easily rationalizable in a game-theoretic framework.

  4. kevin denny says:

    Andrew, I don't think you should think of Levitt as typical or representative of economists even US ones. Some of them may trot out the "its irrational" line but many I know vote for all sorts of reasons, like expressive voting which is perfectly rational. If voting enters my utility function – as chess does- so be it.

  5. Andrew Gelman says:

    Adam:

    If the election is decided by 50 votes, then you're right that your vote won't matter. But if the election is decided by 0 votes, then your vote is decisive! It's an unlikely event but not impossible.

  6. Andrew Gelman says:

    Kevin:

    Sure, but I'm not just saying that voting enters my utility function. I'm also saying that voting (if you live in a swing state) can be a rational way to advance one's political aims (in a low-probability but high-reward sort of way).

  7. Adam says:

    It's true that it is not a priori impossible, but in practice it has never happened and I would be willing to wager a substantial sum that it will never happen.

    But regardless, I see that we don't disagree on the point that had me confused. Thanks for clarifying.

  8. Adam says:

    Reminds me of a debate some public choice economist supposedly (probably allegorically) had. Angry over the idea that one vote wouldn't decide an election, someone said "if everyone thought that way, then no one would vote!"

    To which the economist replied "if no one else voted, I would!"

  9. Jason Kerwin says:

    I don't think Levitt is making this point very clearly. You actually nail it yourself when you say "From the voter's standpoint, a national election is like a lottery." It is not strictly individually rational, in the sense of maximizing objective payoffs, to play the lottery. The same is true of voting. If you care about the social good for the country you'd be better off picking up litter than voting, just as if you care about making money you'd be better off saving than playing the lottery. You're _definitely_ better off not voting if you don't care about other people.

    In both cases it's not quite right to say people are irrational. Rather, factors outside of what social scientists normally consider are entering their utility functions.

    Bryan Caplan explains this quite clearly in *The Myth of the Rational Voter* – the problem is not that voting is irrational, but that it does not conform to the "rational voter model" I was taught in my undergraduate political science courses, wherein voters are assumed to vote in favor of their narrow self-interest. In general it appears people vote because it makes them feel good and because they feel it is a duty. This is clear from asking people, most of whom don't even comprehend the logic of being a decisive voter let alone the probability of that occurring.

  10. Andrew Gelman says:

    Jason:

    No, voting is different from a lottery. In a lottery, the expected return is necessarily negative (except in some rare special cases) because the lottery organizers have to make money. In voting, there's no reason why the expected return has to be negative. In some states there will happen to be very close, high-stakes elections, in which Pr(decisive vote) is pretty high and the outcome is important. In other states, you might be choosing between Tweedledum and Tweedledee and the election might not be close at all. And the cost of voting varies a lot too. Where I live, we just walk over and vote, it's pleasant and it takes about 10 minutes. But I've read that in some places you have to wait on line for an hour to vote.

    Regarding people's motivation for voting: as we discuss in our Rationality and Society paper, rational-choice and psychological motivations can coexist.

  11. Bob Carpenter says:

    Adam: Wagering on something never happening is a mug's game. Without a fixed time frame, you'll never get paid!

  12. David says:

    I haven't looked at you papers on this but do you treat it as though vote are counted with perfect accuracy? Aren't elections that are within a couple of hundred votes of each other pretty much a statistical tie give measurement errors and what would this mean for your results?

  13. Andrew Gelman says:

    David:

    See item 1 in the blog above. Yes, there is noise in the vote count, but your individual vote will still shift the count by +1 or -1 in expectation. Or, maybe, given the possibility of error, the expected shift is .99 or .995 or whatever. In any case, the calculation still holds.

  14. Alon Levy says:

    Another way to think of voting is in terms of collective action. Your one vote may not make a difference, but there's a fairly large contingent of people who think like you, who could be decisive in a close election. For example, those people may be influenced by your example, in which case your act of voting adds more than one vote. It's similar to the decision to join a strike: one more scab isn't going to break the strike, but still it's rational for union members to not scab.

    Moreover, from the point of view of the government, it's very rational to get more people to vote, just like it's very rational for a union to prevent scabbing. So a good government will pass laws making it easier to vote – for example, making Election Day a national holiday and minimizing the hassle involved in registering to vote.

  15. Robert Neumann says:

    Levitt at least makes the valid point that participation in elections is mainly driven by desires unrelated to the actual outcome. That does not mean that one is indifferent about the results of the election. It relates to the argument by Arrow that actual choice is over a set of actions (paticipate yes/ no, vote for party x yes/ no, etc.) but preferences are about consequences. The assumption that the choice to participate in an election is an expressed preference to decide the election or that party x gains more votes is only one part of the story

    There is some evidence that a good chunk of expressed preferences in elections are rather related to consequences such as "support democracy" or "comply with given democratic rules and given opportunities".

    Check here in Rationality and Society (http://rss.sagepub.com/content/22/1/3) for for the interplay on rational incentives and norm driven behavior to explain electoral participation.

  16. Mark Palko says:

    I apologize in advance if I missed this (hey, it's late), but elections are bundled. Once you've cast your vote in the first one, the marginal cost for the other votes is very small.

    So voting isn't like buying a lottery ticket that costs less than its expected value; it's like buying a lottery ticket that costs less than its expected value then getting another five or ten for free.

  17. marcel says:

    I live in Hanover, NH. A few years ago, my wife and I forgot to vote in an election that included whether or not to approve of a new teachers' contract. It lost by 1 or 2 votes. I still regret that mistake. Last fall, across the river in VT, an election for the state legislature was eventually decided by a single vote. At least that is how it now appears. The declared loser lost the recount, and in court, but is taking it to the legislature for review. Since the Democrats currently have a majority in that house of the legislature, and the loser ran as a Republican, I suspect that the outcome will not change, although procedures may.

  18. sj says:

    Andrew,
    I still don't get the altruism, or "add up the utility of every American citzen" argument you're making here. At the end of the day, the simplest "rational choice" question is one about whether the benefits of voting are higher than the costs for people. If the benefits are restricted to only be defined by the chances of affecting the outcome multiplied by the difference in utility between your preferred candidate winning and losing, I don't understand how you can total up the utility over all Americans and have it make sense.
    In particular, if your candidate winning will make Americans in general $1.5 billion better off and you're arguing that this is the number individual voters will plug into their calculation, this implies that if you asked most voters (or a non-trivial number of voters) "would you rather have your preferred candidate win the next presidential election or have him lose and recieve $1.5 billion," they would choose to have their candidate win and leave the money on the table. I'm not sure how you'd test this, but I'd wager that people would usually take the money (I certainly would…).

  19. kevin denny says:

    Andrew,agree totally. Maybe because I'm an economist and a voter I think this "voting is irrational" meme needs to be put in its place.

  20. Tom H says:

    Of the (admittedly few) people that I know who don't vote, not one has said that they don't vote because the probability of influencing the outcome is too low,.

    Most of the non-voters that I know don't vote because they believe the outcome is predetermined: they argue either that the votes are rigged (classic voter fraud) or, more often, that the candidates are already bought and paid for such that, no matter who wins, the winner doesn't represent voters.

    In my opinion, these reasons sound like rationalizations, and the real reasons people don't vote probably have more to do with emotional (de)motivators. Some possibilities have been captured in previous comments, such as a sense of civic responsibility or social expectations to participate.

  21. This move only works if you're pretty sure that your side is the one that makes everybody $50 each better off. But half the population by definition disagrees – otherwise your vote wouldn't be the decisive one, right? How can you tell, ex ante, that you're voting for the team that makes things better rather than the team that makes things worse in that kind of case? If I look out and see that half the folks in the country figure I'm doing something awful by voting for X, why do I think that I'm right and they're wrong?

    Or then suppose you know that you're right and consequently your vote is rational. Doesn't that make all the votes for the other side irrational?

    And how do you know that the half who vote against you won't curse you afterwards for the benefits you purport to bring them if preferences are heterogeneous?

    I think your case requires putting oneself in an epistemically privileged position relative to other voters. If you don't make that move, then you don't know whether your vote tips the balance for better or worse, and the expected value of the lotto ticket you're buying by voting drops to nil.

  22. Andrew Gelman says:

    Eric:

    I think you're overthinking things here. In an election with two options, some people will think candidate A is better for the country, others will think candidate B is better. And of course others won't give a damn at all. If you prefer A or B, sure, if you're sane you'll realize you might be wrong, but your preference is still there in expectation. For example, maybe I'm pretty sure that A is better than B, but I think there's a 20% chance I'm wrong. That's like any decision problem: the existence of uncertainty does not imply indifference. Nowhere did I say that I know I'm right, and in a decision problem there's no need to assume certainty. Not at all.

    Regarding heterogeneous preferences: most political issues are not like abortion where people have completely opposing goals. A vast majority of Americans want peace and prosperity, but people have different ideas about how to get there.

    Finally, my argument applies to all voters who have a preference. Nobody is privileged, it's just that people disagree about who should represent them in public office. There's a disagreement so we have an election. And the same argument applies to any sort of political participation, including campaign contributions, letters to your congressmember, etc.

  23. Addison says:

    How does the altruism addition work in this example :" If you think your preferred candidate could bring the equivalent of a $50 improvement in the quality of life to the average American"?

    What I mean is if I think a win by my candidate would bring a $50 improvement and someone else agrees, does that mean the total value of the win to us is $100? It seems like this could make the dollar value of a win way higher than the actual benefit of the win, since many people's benefit will be enjoyed by multiple altruistic voters.

  24. mat roberts says:

    The whole argument about not voting seems to be based on the premise that "The aim of voting is to cast the decisive vote in the election" – but why is this the case?

    If you applied this argument to football (soccer), it would become "The aim of football is to score the winning goal".

    And then reach the conclusion that the only game an economist would play is where his team has one player – him – and the opposition has none. He could then score his single goal, unopposed, and go home.

  25. Wikipedia has a List of Misconceptions.

    If you think "voting is irrational" should be on it, please contribute to the discussion page.

  26. Andrew Gelman says:

    Turadg:

    I looked up "rationality of voting" on wikipedia and was directed to this page which gives the correct (from my perspective) answer in its final paragraph:

    Another suggestion is that voters are rational but not fully egotistic. In this view voters have some altruism, and perceive a benefit if others (or perhaps only others like them) are benefited. They care about others, even if they care about themselves more. Since an election affects many others, it could still be rational to cast a vote with only a small chance of affecting the outcome. This view makes testable predictions: that close elections will see higher turnout, and that a candidate who made a secret promise to pay a given voter if they win would sway that voter's vote less in large and/or important elections than in small and/or unimportant ones.

    So, at least as far as Wikipedia is concerned, it's not a misconception!

    I would like to correct the misconception that Bayesian inference is all about computing the probability that a hypothesis is true–but I doubt that would get past the Wikipedia committee…

  27. Andrew:

    Indeed, Wikipedia appears to have this issue covered. Yet there is much that Wikipedia knows that people commonly don't, of course. A criterion for getting on the List of Common Misconceptions is evidence that it is, in fact, a "common" misconception. I'm going to offer:

    Don't Vote: It makes more sense to play the lottery (Landsberg in Slate)
    Why do People Vote?: Voting is a supremely irrational act (Psychology Today)
    Why Vote? (Dubner and Levitt in NYTimes)
    Not Voting and Proud: Don't throw away your life; throw away your vote (Reason magazine)

    I'll let you know how it goes.

  28. fraac says:

    Superrationality as taught by Hofstadter and Jesus before him. If I vote for X so will millions of others. If I'm inclined to vote for X but instead stay at home so will millions of other X supporters.

  29. Andrew Gelman says:

    Turadg:

    It's no coincidence, I think, that people who argue for the rationality of voting tend to be social democrats, politically, whereas people who argue that voting is foolish tend to be free-market classical liberals (in the European sense). Examples of the first group include John Quiggin (who wrote a paper similar to that of Edlin, Kaplan, and myself, several years earlier); examples of the second group include the names you give above.

    High voter turnout tends to legitimize the government, whereas low turnout gives the political system less legitimacy. It makes sense that people such as social democrats (and, for that matter, many traditional patriotic conservatives) who are generally in favor of government also are supportive of voting, whereas classical liberals who want limited government would be happier if fewer people voted.

    This is not a perfect connection–I'm sure there are many exceptions–but I think there is something to this pattern.

  30. kmellis.myopenid.com says:

    fraac, I'm not sure why you think that Jesus "taught" superrationality. Maybe I'm forgetting some crucial part of the Gospels.

    It's been many, many years since I read Metamagical Themas, but I don't think that's quite what Hofstadter was arguing in that essay. Rather, it's that one should be aware that one is almost certainly representative of a larger population. One's thought processes, in general, are not unique and therefore one should not imagine that one's own decisions exist without correlation (though not causation!) to the decisions of others.

    In the case of the Prisoner's Dilemma, the argument is that if one is able to recognize that the overall best outcome is for cooperation, and the overall worst outcome is for mutual defection, then one should suspect that the other party may well reason similarly and it becomes rational to choose to cooperate. If one thinks, attempting to be clever, that then one would best then defect, then why would one think the other person wouldn't similarly reason and similarly realize that both are back to mutual defection?

    This seems to many people to seem like a form of magical thinking, where there is a magic causal relationship between what one does and what others do. But that's a misconception.

    I think it's very interesting that you've brought this up and here we are discussing this after we've discussed similar things in the other thread. Hofstadter is very interested in theories of mind. His implicit argument in this is that there's something a little weird about conventional game theory in that it simultaneously posits a perfectly accurate theory of mind for both people (which is to say, they reason similarly and reason about how the other reasons similarly) while also allowing that they make very different decisions. In the PD, both people have exactly the same information. If they know nothing about each others' motivations and reasoning, then they can't conclude anything at all, not even how the other would relatively value the different possible outcomes. It's assumed they know things about each other, assumed that they share similar motivations and reasoning. But to the degree to which this is true, is the degree to which they will come to the same conclusion about the best possible choice. It's not exactly clear how it is that one person would believe the other would choose to cooperate while they themselves would choose to defect.

    There is some essential weirdness about theories of mind that has everything to do with the weirdness of self-reference. When we say, "if I were you, I'd do X", it's very unclear about what we think we are saying, and it's very odd.