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Why it can be rational to vote

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!)


  1. harryhaller says:

    what damage have older white people done to this country? :)

  2. David Marcus says:

    It is rational to vote if you believe there are other rational people. This is just the resolution to the Prisoner’s Dilemma paradox. It is the same reason that it is rational to wear a mask during a pandemic, even though the benefit of the mask is mainly to other people: If we all do it, then we can control the pandemic. Unfortunately, some people aren’t rational, so we must enforce mask wearing by additional means.

    • jim says:

      “Unfortunately, some people aren’t rational, so we must enforce mask wearing by additional means.”

      Hilarious. What was that experiment where first they gave people some purported irrefutable claim from scientific authority figures and measured how many people “bought” it. Then they told people “no, we lied to you about that to test you. Here’s what scientists really said”. Then when people rejected the new purported irrefutable reality, the experimenters concluded they had “cognitive dissonance” and irrationally rejected science! Hilarous. Give people a purported scientific claim. Then tell them you lied about it and give them another one. Then claim they’re stupid because they don’t accept the second one.

      Dang, I wish I could remember that experiment.

      Not that I don’t support mask use. I do. But let’s not forget how vehement authority was about how useless masks supposedly were. Since not everyone has a degree in science to figure out how and why masks actually work, let’s forgive people for at least some of their skepticism and put some of the blame back where it belongs – on the people who screwed up in the first place.

      • Tom Passin says:

        “Not that I don’t support mask use. I do. But let’s not forget how vehement authority was about how useless masks supposedly were”

        The early guidance in the US was mainly not that masks are useless, but that we had so few that they should be saved for medical personnel.

        • Anoneuoid says:

          The guidance was that masks are dangerous for the general public. You can easily look up the surgeon general, etc saying so.

          Seriously people- STOP BUYING MASKS!

          They are NOT effective in preventing general public from catching #Coronavirus, but if healthcare providers can’t get them to care for sick patients, it puts them and our communities at risk!

          Surgeon General Jerome Adams Tuesday doubled down on his advice against healthy people wearing face masks to protect themselves from coronavirus, saying that wearing one improperly can “actually increase your risk” of getting the disease.

          “What the World Health Organization and the CDC have reaffirmed in the last few days is that they do not recommend the general public wear masks,” Adams told Fox News’ “Fox and Friends.” “There was a study in 2015 looking at medical students. And medical students wearing surgical masks touch their faces on average 23 times. We know a major way that you can get respiratory diseases like coronavirus is by touching a surface and then touching your face.”

          Masks also can give the wearer a “false sense of security” and can encourage people to be too close to each other, said Adams, and further, there are still mask shortages nationwide.

          People who are sick should wear masks, said Adams, but acknowledged that if healthy people feel better by wearing a mask, “by all means, wear it” but they should not touch their faces.

          He also insisted the general public should not wear medical-style N95 masks, because they must be fitted properly to avoid infection.

          “There may be a day where we change our recommendation, particularly for areas that have large spread going on, about wearing cotton masks but again the data is not there yet,” said Adams.

          Do people really have no memory of what happened just last spring?

          • Dale Lehman says:

            Do you really equate the Surgeon General with “vehement authority?” There are so many politically motivated people in authoritative positions, that you can find virtually any position stated by someone at some time. I don’t believe the statement that authoritative voices were generally saying masks were bad accurately reveals what happened in the spring. There were mixed and poorly worded messages, but I think the prime motivation was to preserve masks for first responders when there was a shortage. The general position of experts fairly quickly emerged that masks were useful and important – not sufficient in themselves, and certainly not without risks if used badly. But to equate a Twitter statement from the Surgeon General as definitive authoritative advice is a misreading of the actual events. You say “Do people really have no memory of what happened just last spring?” My answer: you have a particularly selective memory.

            • Anoneuoid says:

              Do you really equate the Surgeon General with “vehement authority?” There are so many politically motivated people in authoritative positions, that you can find virtually any position stated by someone at some time. I don’t believe the statement that authoritative voices were generally saying masks were bad accurately reveals what happened in the spring.

              I dont consider any of these organizations an authority on health but it was the same message from the surgeon general, CDC, and the WHO. I quoted it right in that post.

        • Bill says:

          The message was badly worded; but in the case where you have a scarce and essential resource, the right thing to do is to use that scarce resource where it will do the most good. Keeping medical personnel safe in an environment where infection risks are high and medical personnel are essential do deal with the situation was clearly the right decision.

          They should have been more clear than they were.

          As it was, instructions on how to make masks were readily available and we made and used our own, thus not affecting the situation in medical facilities. Locally, a group got together and made a large number of masks and gave them away for free in our (smallish) village.

          • Steve says:

            The guidance was terrible, and there was no scarce resources. Cotton cloth is not scarce and anyone with a sewing machine can make a reasonable useful mask, which is what happened. Don’t defend the indefensible. This was just an example of an overly narrow definition of “evidence” that the “evidence based medicine” movement has given us — where evidence is something published in a journal. Anyone could have taken a spray can and a mask and done a little experiment to show that mask limit the spread of at least water droplets. What more evidence is needed.

            • Anoneuoid says:

              I was thinking the other day I’ve never seen a blinded RCT that putting ice cubes in your drink cools it down. Everyone is doing it and risking cracking a tooth based on anecdotes. Worse, even if they heard it cools down orange juice, I’ve seen them assume it will also cool down a lemonade.

              The problem with masks is in the details though.

              1) Most people are not wearing them properly and touching their face more often, etc. I have also been in ubers where the driver wears the ones that concentrate and vent out their breath, so that isnt protecting anyone.

              2) Some of the most popular ones (neck gaiters and bandanas) can aeorsolize the respiratory droplets making the wearer a superspreader,

              3) They can accumulate bacteria and increase chances of bacterial pneumonia in susceptible people.

              4) A false sense of protection, since even the surgical masks really only reduce transmission by 50% or so.

              5) For it to be effective the population immunity to many different pathogens is dropping at the same time by supposedly the same 3x it achieves for covid (along with lockdowns, etc). This may and up a big problem for all the people who have been staying home for almost an entire year or more now.

              • Steve says:

                All of these are problems that could have been addressed by national health officials with better guidance. That is what should have happened.

              • Anoneuoid says:

                All of these are problems that could have been addressed by national health officials with better guidance. That is what should have happened.

                Well Ive been railing against NHST and so called “evidence based medicine” for about 5 years now and saying if it ever came down to it the medical community would be an epic fail that could destroy western civilization.

                Fisher warned us back in the 1950s:

                “We are quite in danger of sending highly trained and highly intelligent young men out into the world with tables of erroneous numbers under their arms, and with a dense fog in the place where their brains ought to be. In this century, of course, they will be working on guided missiles and advising the medical profession on the control of disease, and there is no limit to the extent to which they could impede every sort of national effort.”

                Fisher, R N (1958). “The Nature of Probability”. Centennial Review. 2: 261–274.

                One reason I quit medical research because I didnt want to be blamed for this.

            • Bill says:

              There’s a big difference between masks used as PPE by medical personnel and the kind of masks you can make from readily available cloth and a sewing machine. The initial reaction, which was poorly worded and explained, was to keep the high-quality masks used as PPE by medical personnel from being snapped up by everybody else, and because of the short supply of these specialized masks, become unavailable to those that needed it in high-risk medical situations.

              They should have been more clear in what they were concerned about.

          • Martha (Smith) says:

            “As it was, instructions on how to make masks were readily available and we made and used our own, thus not affecting the situation in medical facilities. Locally, a group got together and made a large number of masks and gave them away for free in our (smallish) village.”

            Yup. I made my first two masks, using instructions on the web. And a cousin made lots of masks and shipped them off to relatives who were medical personnel but were experiencing mask shortages where they worked. (I also improvised with bandanas — I found that a certain configuration of hair clips was good at keeping them in position. I still use them sometimes.)

      • Joshua says:

        jim –

        > But let’s not forget how vehement authority was about how useless masks supposedly were

        Let’s not forget how many snowflakes are acting like wearing a mask is some huge inconvenience or even more bizarrely, some huge infringemwnt on their civil rights and liberty – as if they have the right to infect other people needlessly and that doing so is a fundamental freedom.

        What makes it even more bizarre is that they argue that they’re willing to take the risk, as if wearing a mask has nothing to do with them putting others at risk.

        • jim says:

          Well that sparked a little more discussion than I anticipated.

          “Let’s not forget how many snowflakes are acting like wearing a mask is some huge inconvenience or even more bizarrely, some huge infringemwnt on their civil rights and liberty”

          I agree. That is bizarre and hilarious. But there is a context for it: a) the left wing assault in individual rights and speech; and b) the increasing failures of the “expert” establishment.

          “as if wearing a mask has nothing to do with them putting others at risk.”

          From what I understand the consensus among sensible non-screamers is that masks provide a modest extra margin of protection, so on the flip side the lack of a mask generates a modest extra risk.

          Again, I think people should wear them. But on my hike last Sunday it was pretty clear trail mask etiquette has declined significantly even up here in the Seattle Leftopia.

          • confused says:

            While I don’t really agree with the political aspect here (I do agree that people should wear them, and that the benefit is likely modest — at least in the sense that they are neither “useless” nor “totally protective”) I think you are correct as to *why* people act this way.

            Specifically it’s the “expert” issue – many people IMO feel that government decisions are being driven by experts whose basis for decisions are not really transparent to the public due to the nature of models, etc.

            So the average member of the public (and perhaps even the elected officials) do not have the knowledge base to know whether the decisions being made are sensible or not. It’s a “fear of being scammed” in a sense.

            The American individualist streak makes this especially strong here, and IMO much of the early messaging did not take this into account.

          • Joshua says:

            jim, confused –

            > Specifically it’s the “expert” issue –

            I think you kind of have the direction of cauality wrong. People pick and choose their “experts” depending on what they want to hear, where they align the “experts” in their political eco-sysyem.

          • Joshua says:

            jim –

            > But on my hike last Sunday it was pretty clear trail mask etiquette has declined significantly even up here in the Seattle Leftopia.

            Here in the lefty regions of the Hudson Valley, masks are still quite uniformly worn. I think that lefties are hearing from “experts” they trust that outside there isn’t much risk. I don’t think there’s an overall decline in mask etiquette -even if there is a decline in trail mask etiquette.

    • Andrew says:


      Even if you don’t think other people are making their voting decisions rationally, it can be rational for you to vote because of the small chance that your vote is decisive, leading to a large effect on the world.

      • David Marcus says:


        Yes, you can make the numbers work, but that is not nearly as good (or as rational) a reason to vote. I don’t see people going around handing out your calculation to convince people to vote. The reason that people give to vote is basically what I said: We should all vote so that the candidate we know is better will be elected.

        It is the same as the Prisoner’s Dilemma. Each prisoner thinks he should defect, but once they realize that the other prisoner is thinking the same, they realize that they will do better if they cooperate. Real criminals manage to figure this out, but it seems to be hard for mathematicians to figure it out. The Nash equilibrium is so seductive, but the definition doesn’t say that the Nash equilibrium is optimal.

        You just have to realize that if we all do it, then things will be better than if we don’t. Of course, for elections you don’t have to have rational people. You just need to get a large group, e.g., a political party, to pool their efforts and all go vote.

        I find this helpful when deciding how much money to contribute to political organizations. I can’t give enough money to individually make a difference. I could do a calculation similar to your voting calculation, but I don’t think I’d believe the number I got. So, I try to imagine how many people support the cause and so how much it is reasonable for each person to contribute.


          • David Marcus says:

            There is a village of mathematicians and a castle with a vampire. The mathematicians hold a meeting and agree

            1) It would be good to get rid of the vampire.
            2) If we all storm the castle, we can get rid of the vampire.
            3) If all but one of us storm the castle, we can get rid of the vampire.
            4) The castle stormers will meet at 9 a.m. in the morning.

            Since they are mathematicians, they don’t bother to state the conclusion, but just assume that everyone will figure it out for themselves.

            Andrew says that they each need to go home and do a cost-benefit analysis to determine whether to go to the 9 a.m. storming.

            I say that they should each go home and realize that all of them storming the castle is better than none of them doing so, and so everyone should show up for the 9 a.m. storming.

            • Andrew says:


              You misunderstand. I’m not saying that people “need . . . to do a cost-benefit analysis.” People vote for all sorts of reasons. I’m saying that, if you want to evaluate voting using a cost-benefit analysis, here’s how to do it. This is relevant to the poli sci and econ literature because there’s been a very influential view in those fields claiming that voting has no instrumental benefit. Our work is addressing that literature; it’s not saying that individuals need to make this calculation.

  3. Aleph Naught says:

    A consequentialist case for voting has to account for two types of uncertainty—uncertainty about whether one’s vote would be decisive, and uncertainty about the consequences of one’s vote being decisive. The unpredictability of the future means that my candidate winning may set in motion all sorts of unanticipated consequences, which in the fullness of time may prove to be arbitrarily bad, or arbitrarily good. Being ‘well-informed’ just means having a command of current theories of how some things work, not understanding how things actually work in a way that allows for any confidence that the all-things-considered impact of getting my way will be better or worse than the alternative. By contrast, the cost of voting, while trivial for most people most of the time, is quite certain.

    • Bill says:

      There are two aspects to any decision. One is the probability (in this case that your vote makes a difference). The other is the loss or utility function (how important it is if the result goes one way or the other.)

      Andrew is exactly right to evaluate both of these in a way that makes sense in the context of classical decision theory.

      • Aleph Naught says:

        Not sure what you’re disagreeing with in what I wrote, Bill.

        I agree that, if the the case for voting is consequentialist, we have to consider the probabilities of different scenarios, and evaluate a utility function in each of these scenarios. I agree that Andrew is making an argument of this form.

        What I’m disagreeing with is stipulating that in the extremely improbable scenario that one’s vote is decisive, the utility of one’s favored candidate winning yields enormously greater utility than the alternative. I’m disputing this because I’m suggesting that there is paralyzing uncertainty about what the future consequences of this would be, such that assigning this substantially greater utility is not reasonable. (The utility of your candidate winning in this type of calculation is itself an expected utility, with probabilities over the different ways the future of the world might unfold in that scenario. It’s these second set of probabilities I’m saying are almost maximally entropic given the unpredictability of the future.)

        • Bede says:


          You have a rather generic criticism of the utility of utility theory, and decision analysis in general. What are you contributing to the discussion? All you are saying is that according to your criteria, decision analysis in practice is useless. Yes, any agent that cares exclusively about the terminal nodes in her lifetime decision tree (or humanity’s) would be making a mistake to optimize today’s choice (time t) based only on the consequences at time t+n nodes (n fixed). If this is your approach, all applications will miss the mark. But we live in this world, no need to feel paralyzed because it is possible that voting for the candidate you think will be destructive could actually be a good thing in the long run. Once you decide that Biden > Bush, we can begin to analyze the problem. Why is that so hard?

          • Aleph Naught says:

            Bede, this is a generic criticism of utilitarian thinking, but it’s not a generic criticism of decision theory. The critical difference is that, in Andrew’s application, he’s asking us to consider the impact of getting our way not just on our own lives, but on the lives of all Americans. But why stop there? What about foreigners? Future generations? And so on. The more we expand the circle of interests factoring into the calculation, the more hopeless it becomes to determine whether one person winning would lead to massive benefits relative to another person winning, all things considered. The problem becomes much easier when we consider the impact of an election outcome on ourselves, or our immediate family members, or our local community, etc. It also becomes easier when we focus on relatively short-term impacts. To be sure, it’s still very hard, but it’s easier. And everyday decision analysis (e.g., should I reduce how much coffee I drink everyday?) is easier still. So you’re right that this is a generic problem, but the way Andrew wants us to conceive of *this* decision problem, we end up with the most severe version of this problem, while for local, self-interested, everyday decisions, this problem remains but is far more manageable.

            • Andrew says:


              When deciding what brand of car to buy, or whether to buy a car, it makes sense to think about the immediate impact on my family and only then on larger impacts, because the impact on my family is direct. When deciding who to vote for, or whether to vote, it makes sense first to think about larger impacts, because that’s what the outcome of the election will affect.

              • Aleph Naught says:

                Andrew, I agree. My point is that your argument works by saying, while the probability of being the decisive vote is very small, the benefit of being the decisive vote might be very large, but I don’t know how one could reasonably come to the latter conclusion. If we only ask very specific questions (what impact will the election have on the rate of uninsurance among US citizens?), then we can sometimes arrive at well-informed answers (the Democrat will probably reduce said rate, the Republican will probably increase it). If we ask questions about the all-things-considered impact of an election outcome, we rationally will find ourselves unable to make any specific prediction. This is precisely because elections have large impacts on everyone, here and abroad, now and into the future, and our understanding of such impacts is primitive at best. By contrast, when buying a car, the considerations in play are narrow, and we can make fairly specific predictions confidently. The problem is not decision analysis, the problem is applying decision analysis in situations where the informational demands it places on us far outstrip the information a rational, well-informed voter actually has.

              • Andrew says:


                Agreed. When it comes to societal benefits, it’s all very speculative.

    • Joshua says:

      Even if one’s vote isn’t decisive it can still have a (marginal) impact.

  4. Anoneuoid says:

    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).

    I’ve never been polled and don’t know anyone who has told me they’ve been polled. I doubt I know someone who *would* be polled just because they are educated enough to not click random links online (or don’t use the internet) or answer phone calls from strange numbers let alone give out personal info to them.

    Whoever is getting polled is part of some entirely different age group or subculture from anyone I know.

  5. Dale Lehman says:

    Why all this attention on whether or not voting is rational? Sure it is an interesting theoretical question with practical importance. But it is not the complete picture. Not everything we humans do is, or should be, rational. Some irrational things are done for different reasons. For example, helping a stranger in need is generally done for a variety of non-rational reasons. You can try to torture the explanation to be “rational” (e.g, by saying that acting kindly will result in others acting kindly towards you when you are in need – arguable at best – or just simply saying that being kind is in your utility function, hence it is rational to satisfy your preferences), but there is no need to do that. The downside of trying to make everything rational is that we start believing that rationality is a singular goal worth pursuing. I like to hold onto the belief that some things are worth doing just because they are the “right” things to do. No rationality required.

    But, on what basis do we decide what is “right” if it is not rational? After all, plenty of horrible things have been done by people because they believed they were “right” on the basis of religion, cult, tribe, etc. This seems to be the ultimate human dilemma: how do we establish ethical beliefs without needing to invoke rationality? Or is that even desirable? I can’t answer those questions, but I feel that having an answer that does not require rationality is somehow critically important.

    • Steve says:

      Dale says, “Not everything we humans do is, or should be, rational. Some irrational things are done for different reasons.”

      I think that you are using “rational” and “reasons” in an ambiguous way. If I do something for a reason, then I am acting “rational.” If I define the reason to act as maximizing my expected return of utility, some actions look irrational. But if I define my reason for acting as maximizing the social good, then that same action can look rational. In contrast, my reason to act may be to bring about a future state that I believe to be superior to the current one. I may not be able to model that in terms of maximizing a single quantity, but I can still model how that action brings about that preferred state. The only time, a person is truly irrational is when the reason, i.e., the goal of their actions is not consistent with the action taken. However, only the actions that the take are empirically observable. Their intentions are not. Thus, we can always reinterpret people as acting rationally, by reinterpreting what goals they are pursuing. Thus, the futility of these constant arguments about whether people are “rational.”

      • Garnett says:

        This is very well put. +1

      • Dale Lehman says:

        Yes, words are ambiguous. You say “the only time a person is truly irrational is when the reason is not consistent with the action taken.” I guess I can agree with that. But, I recall one highly educated Trump supporter saying that she supported him because he has restored dignity to the White House. I choked on that. But, I’m fairly certain that she would say her reason (restoring dignity) is consistent with her action (supporting Trump). I guess evidence is also ambiguous.

        In the end, this discussion ends up with irrationality only present with particular mental illnesses. But if almost everythign is rational, then debating whether voting is rational or not is a pretty meaningless discussion. I think asking “should I vote?” is a much richer thing to discuss than whether or not it is rational.

        • Steve says:

          Dale says: ” But if almost everything is rational, then debating whether voting is rational or not is a pretty meaningless discussion.”

          I don’t think it is meaningless. It is meaningful to ask, how can I explain how these people are acting if I assume that they are acting in a way consistent with their goals. I then can hypothesize what their goals are from their actions, and perhaps predict their future behavior to some extent. So, the Trump supporter doesn’t mean the same thing that you mean by “dignity.” What does she mean, a certain way of acting that is seen as strong and patriotic in some subculture of America. That could be a very useful insight. On the assumption that people are acting irrationally, their behavior becomes intractable and impossible to predict. Again, they may be irrational, but it is a hypothesis that (mostly) leads no where.

  6. #1621A314 says:

    Your personal vote has no effect on election outcomes; check the official government stats on every election you’ve ever voted in — and it’s blatantly obvious that the presence/absence of your vote made no difference to outcomes.

    But the big problem is that you, Mr/Ms Citizen have no actual control on the complex actions of the many government personnel who will daily rule you for years.
    Elections are, at best, an extremely indirect and weak mechanism of control upon the government employees who exert very large effect upon your life.

    The “Theory” of U.S. citizen control over large government institutions (city/state/federal) is totally bogus.
    Today’s events are more akin to a tribal ritual.

    • Andrew says:


      You say, “Your personal vote has no effect on election outcomes.” That’s not correct. There are occasional tied elections. In addition, there’s a small chance that your personal vote can effect a large election. It’s a small chance but it’s not zero. Suppose I went to half court and heaved a shot. I’ve never made a half-court shot, but the probability of my heave going in is not zero.

      • Steve says:


        You write, “It’s a small chance but it’s not zero.” Isn’t the case stronger than this? As I wrote below, doesn’t backward induction show that voting dominates over not voting if we are maximizing the public good. Knowing that my vote counts for almost nothing, I decide to sit this one out, but then I realize that everyone is similarly situated and will also sit out the election, making my vote the deciding one. Of course, everyone will realize what I just realized and vote. So, I can vote and be the deciding vote or vote and have only a small chance of deciding the election, but that dominates over not voting when my vote was the deciding vote and not voting where my vote had a tiny but still positive chance of being the deciding vote.

        • Jonathan (another one) says:

          The notion that things that you do induces other like-minded people to do the same thing is a version of Newcomb’s Paradox…. and borderline crazy.

          • Steve says:

            It has to do with the reasoning not reverse causation. Backward induction is a standard concept in game theory. Knowing that if I make a certain move you will make another move to counter it that will put me in a worse situation is how anyone playing any strategy games reasons.

            • Jonathan (another one) says:

              And of course there are plenty of paradoxes in backward induction as well… the unexpected exam being the most well-known example. But I’m making a simpler point, since the defector here is *not* in a worse position by not voting, except in the situation (as Andrew points out) in which they are pivotal. Thus, why one should vote in CA or NY or DC remains unexplained.

              • Jonathan (another one) says:

                The notion that there are enough people in NY who reason not just somewhat like me, but *exactly* like me, to make a difference in the outcome of NY’s electoral votes is what’s borderline crazy. It’s like saying that a fireman should go vote because if he doesn’t go vote not enough firemen will vote. There is no basis for the synchrony of decisions.

              • Andrew says:


                I agree with all of your reasoning. But, just to be clear, why one should vote in CA or NY or DC is not “unexplained.” There are lots of good reasons to vote in CA or NY or DC. It’s just that the possibility of swinging the national election is not one of these reasons.

                One quick reason for voting, wherever you live, is that voting is a habitual action. It’s a good idea to get into the habit of voting because it might come in handy some day. Another reason for voting is if you feel you are voting as part of a group of similarly-minded people. If enough people like you around the country vote, this can make a difference, and you can feel there’s an implicit compact for all of you to vote. Yes, defecting would be ok, but defecting isn’t an option if you’re making the decision at the level of whether to join the compact rather than whether to vote this one time.

                This is related to the advice to evaluate the strategy, not the play.

              • Jonathan (another one) says:

                Yes, you’re right, Andrew. I meant “unexplained by the very logical argument you make about why it’s rational in swing states.”

              • anon e mouse says:

                To add to Andrew’s list of reasons, I find that even in California at least one local race or ballot measure often comes down to a very small margin where the result can’t be determined until every last ballot is counted. To give a current example, in my jurisdiction we have no primary for local races, so there are a double digit number of mayoral candidates on the ballot. It’s very possible the margins in that race will be quite small, as the race is nominally non-partisan, there’s no incumbent, and several candidates have some name recognition.

              • Jonathan (another one) says:

                The easiest explanation of why it’s rational to vote in CA or NY is that you have downballot races for things like mayors and the like where the social payoffs are much lower for being pivotal, but the chances of being pivotal are much higher. And once you’ve incurred the fixed costs of voting, filling out the Presidential box are close to nil.

              • Andrew says:


                In addition to all that, it’s very rare that we have close downballot races where I live! We did have a close race for mayor many years ago, and then more recently a couple of state legislative primaries which ended up not being very close but had high uncertainty before the election. That was about it.

  7. John Williams says:

    I was with you until I got to “So, yes, if you are in a district or state that might be close, it is rational to vote.” I live in California, so my vote for Biden didn’t mean much, but I also voted on a bunch of other candidates and various propositions. Beyond that, politicians pay attention to voting margins (I used to hold a local elected office, so I know that from personal experience).

    • Z says:

      I think in Andrew’s longer version of this he goes into the probability that your vote changes the rounding of the percent margin of victory in the popular vote, impacting the sense of a mandate.

    • Steve says:

      John says, “I was with you until I got to “So, yes, if you are in a district or state that might be close, it is rational to vote.”

      +1 Won’t an argument from backward induction prove that it is rational to vote in a state where Biden is going to get a large margin show that it is rational for me to vote if I am trying to maximize the public good, i.e., if I don’t vote for Biden, he will still win, and the public good will be unchanged. But, what is true for me, is true for every other Biden voter in New York. Therefore, no Biden voter should vote, but then Trump voters realizing that Biden voters won’t vote in New York because it won’t change the public good in their favor, should vote. But, then Biden voters realizing that every Biden voter will not vote on the logic that their vote doesn’t matter, will see that not voting will effect the public good negatively. Therefore, it is rational to vote even where the likelihood of my vote mattering is small. Am I missing something?

      • Jonathan (another one) says:

        As I said above: Newcomb’s Paradox. What I do has no effect on what like-minded people do. That breaks the backward induction.

        • It’s not what you do affecting others, it’s the reasoning you use to get to the action.

          First order reasoning: if you vote, nothing will change. At the margin for just you, this is true

          Second order reasoning: if most people think like the above, then something WOULD change for the worse, therefore you shouldn’t think like the above…therefore you should vote.

          • Jonathan (another one) says:

            Third order reasoning… I can safely defect from the fools who stop at second order reasoning.

            • rm bloom says:

              Fourth order reasoning: if sufficiently many do just that, they set an example. And then the elections are dominated by those “fools” who don’t know better than to waste their time voting.

              The thing is a pseudo-paradox: the ones who do not vote do actually cast a vote: for the winner!

  8. I don’t have time to reply to all the comments, but I was inspired by the two articles cited and have been pushing this idea for a while. In recent talks (listed in my web site) I have taken this analysis one (obvious) step further. The effect is even larger if you consider the whole world now and in the foreseeable future. If your utility for other people’s utility is roughly constant (regardless of the number of them), then a situation can arise in which it is rational to vote for a candidate or proposal who will best serve the world yet not rational to vote at all if you consider only yourself or your nation. More generally, such “cosmopolitan” voting is more efficient than nationalism or self-interest. And, although I’m sure that practically nobody has done the calculations, lots of people think this way. (Greta Thunberg and Pope Francis come to mind.) See the work of Nancy Buchan for “real data”.

  9. Mike Deigan says:

    “If your vote is decisive, it will make a difference for 300 million people.”

    As Jonathan Baron points out, this is a significant underestimate, given how much US policy decisions affect people in other countries and (potential) future people.

    Most notably, I expect Democrats being in control of the White House and Congress will reduce harms from climate change and the existential risks from climate change and nuclear proliferation (see Ord’s recent book The Precipice on existential risk and its importance). This means that a tiny chance of a decisive vote has rather high expected value, even putting aside benefits to current citizens.

  10. jonathan says:

    You apply a limited definition of rationality. I can understand specifying the decisive case as being rare. But when you reach the next step, you’re talking about your relationship to putative aggregate effects. Why is that a logical cut?

    An example is a lottery ticket. You can specify the rational decision based on the size of the pot versus the odds and come to a calculation that yes, the chance of a payout is more than my $1 or $2 investment. But of course people dont actually use that form of rationality; they use a form that says ‘a lottery ticket is no different from a good cup of coffee or maybe a beer or some fries’, meaning there’s enjoyment in the act. If you pay $5 for a latte because you want to feel good and, back in the day, you could engage in some banter or other conversation – or maybe you just stare at tiktok videos for 10 minutes – then why not a dollar that gives you the entertainment of thinking about having millions of dollars all of a sudden.

    This suggests a logical cut is that it’s fun to be involved in the process. People get excited. Supporters used to fight on the streets before elections in this country. This is a game and you have the chance to buy a ticket for the investment of some time.

    Note for example that I live in MA. I vote but my enjoyment or involvement level is describably different than someone who lives in a more toss-up state. So one can make a cut by the nature of races. But though Markey is going to be senator, we dont know who else will be senator. So my voting ‘says’ I’m participating in the larger game though my vote is entirely meaningless in the most limited terms because the Democrats nearly always win MA. The one big exception shows my point: Scott Brown was elected because he drove a pickup truck and that symbolized anti-Washington sentiment post the enactment of Obamacare. (Even here, Obamacare caused the Democrats to lose ground, which might be a lesson to remember.) One could say ‘only vote when you really, really care’ but that imposes an additional requirement to the simpler point that voting means you participate in a game in which you have varying levels of ‘meaning’. That your vote has varying levels of externally determined meaning may affect your enjoyment or other feedback from voting – which could be anxiety over outcome, etc. – but you cant say your internal responses are eliminated by being one of millions of votes in safe Democratic Party held areas. Otherwise, why pay $5 for a latte when you could have gas station coffee that you sip while standing outside flapping your arms to stay warm? Everything’s the same, right?

  11. J. J. Ramsey says:

    There was a “Demotivator” poster that said “No single raindrop believes it is to blame for the flood,” and I take that as a model for why one should vote, even if that vote is unlikely to be decisive. Each vote is a “raindrop,” so to speak, and if I want a “flood” of votes to happen, I need to at least do my part and cast my vote so that it is part of that “flood.”

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