A Poll Tax on Selfishness

On a wintry night a few weeks ago, I was walking with Aaron Edlin across the Harvard campus when he casually claimed that the “voter’s paradox” wasn’t generally true — that it could be rational for people to vote for purely instrumental reasons.

I did a double take, because the chance that my vote will change the result of any election in my lifetime is vanishingly small. People might vote because it gives them pleasure, or because of its expressive value, but most economists think that it would never be worth your while to vote in order to impact an election, because of the small probability that any one vote is “pivotal.” But Aaron, together with co-authors Andrew Gelman and Noah Kaplan, has written a very important article showing that it can be rational to vote if you care about other people. If you care even a little bit about the welfare of your fellow citizens, then as the electorate increases, even though the probability of being pivotal becomes small, the impact of being pivotal becomes large. Thus, it can be instrumentally rational to vote even in winner-take-all elections with very large number of voters.

This claim, at first, struck me as being true, but too cute. However, the article does have the following interesting implications:

1. As voter turnout drops, the probability of being a pivotal voter increases, while the benefits of being a pivotal voter remain constant (being a function of the number of people in society, and not the number of voters). This means that there will be a smaller turnout in regions in which socially minded voters find it worthwhile to vote.

2. The model also explains, from an instrumental perspective, a new reason why voters may care about electability. In the voter’s paradox world, it is hard to figure out not only why people vote, but why they vote for candidates who are not their first choice. Under the old view, since there was (almost) no chance that your vote would matter, if you voted, you might as well have expressed support for the candidate you liked best. But Edlin’s model suggests that the probability of being pivotal will be higher for one of the dominant two candidates than it will be for a third-party candidate. So Edlin voters might find it rational to vote for second-best candidates who have a higher chance of winning.

Still, to my mind, the neatest implication of the model is that it suggests that publicly minded citizens will have a much larger say in our polity. In Edlin’s model, selfish citizens will not vote, and publicly minded citizens will. Indeed, the more you care about your fellow citizens, the more likely you are to vote.

The unwillingness of the U.S. system to bribe people to vote, or (as Australia does) punish people who don’t vote, operates as a kind of a poll tax on the selfish citizens who care only about themselves. Is it a good idea to promote this kind of selfishness selection, or should we mandate (or affirmatively incentivize) voting? I’m not sure. But whether it is good or bad, the systematic censoring of selfish voters is something that has big implications for the kinds of policies we would expect government to adopt.

So if you live in Ohio or Texas (or Vermont or Rhode Island), and if you care about the welfare of your fellow Americans, make sure to vote.

Kevin L.

This result appears to me to be both trivial and nuts. It is nuts t0 assume that the amount you care about an election is linear in the size of the country you live in. Does any rational person believe that Canadians should have only 10% concern about their elections as the USA? Even for the socially minded individual, there is a saturation at large numbers.

However, if you make the assumption, then the result is trivial. If you have a true toss up election, where 50% of the electorate favor each of two sides, then the probability that your vote will be decisive (i.e the final tally will differ by zero or one without your vote, is on the order of 0.4 divided by the square root of the number of votes cast, since the square root gives the standard deviation of the expected real vote distribution. If the gain scales linearly with the number of people, then the gain from tipping the election times the probability of doing do will grow as the square root of the population size. However, if as is realistic, the gain from tipping the election saturates, then the gain from voting will go down as the square root of the population size.

Voting probably costs the average voter on the order of one half hour of their time (including transportation to and from the polls). Those above who claim that voting has negligible cost obviously don't value their time very highly!


Nichole Harper

I am truly shocked that apparently no one bothered to point out that by not voting you are, in fact, expressing a political statement. The assumption that people do not vote because they are selfish or do not care about the electoral system is ridiculous. One can consciously decide not to vote for any of the candidates and still be glued to the television and newspapers during elections.

Here is a question to ponder for a while: Would more people turn out to vote if the ballot was designed to reject the 'perceived' worst candidates or include a vote of no confidence in any of the candidates?

~Nichole Harper


Why then are there many people who vote in the general election but not in the primary? The benefit to society is the same and the probability of the vote affecting the outcome is larger than in the general election. It seems that this model must still, for many voters, rely on an intrinsic pleasure derived from voting.

ML Harris

I for one support the economist's view of voting. It makes no sense for the large mass of people to vote, since their votes will not count. I especially support this view for republican voters, but that's a side story.

Please, all of you in red states, be rational, don't vote, as your vote won't matter. And let all of us public minded people have a greater effect on the election. It might be a road to better policy. Probably not.


The Times gives you a blog for this?



An analogy: Imagine a famous author writes a book that you really want to read. The author has said that he will post the book on the Internet if he gets 100,000 donations of $1 each. If he doesn't get 100,000 donates, he will destroy the book.

Is it rational to contribute a dollar even though, most likely, that dollar won't be the deciding dollar that puts it over the top?


Actually, the lifetime odds of being "the" pivotal vote aren't as low as they look, because every single person on the winning side is "the" pivotal voter in a close race.

A few years ago, there was a municipal election about two towns over from me that was (at least according to initial counts) won by a single vote. Every single one of the voters for the winning side could be justly considered "the" pivotal voter. So we're really looking at the low odds of a single-vote election difference, times all the hundreds (or thousands) of people who voted on the winning side for that election.


You should vote for the candidate who you agree with most closely, even if they are not likely to win. The more votes they get, the more future politicians will change their platform to capture those votes.

For example the 1928 Socialist party never won anything, but influenced future politicians who eventually implemented almost every plank of their platform.

Jason L., Founder Prapta.com

We're still going to need a few more books published and more equations to get more people to vote.


Whatever the attractions of the model it says NOTHING about selfishness:

Selfish voters may place extraordinary value on the outcome (and hence derive value from voting) because of:

- a moral/values-based issue that is important to them personally

- a wish to inflict punitive measures on the criminal, feckless, lazy, foreign, or any other group that is perceived to benefit from government largess...


I always look for two results in an election - Who won and by how much. If the swing is huge, then the politician in power claims a mandate and does whatever they want. Close, and there may be a bit more navel gazing before legislation.

Thus my vote counts


The voter's paradox is only a paradox if you fail to take into account the moral nature of most humans. That is to say, unlike what psychopaths such as M. Friedman and his followers, we tend to act as we would want others to act. You know, the golden rule? Well we vote because it's the moral thing to do, since when more people vote it's good for society as a whole, and bad when fewer do.
It's odd that evolutionary biology, which is often (wrongly) summarized as the "struggle for life & survival of the fittest", should have no problem dealing with this (see Dawkins' _Selfish Gene_) while economics still can't figure that out.


Have to say this to and fro is one reason why ordinary people have doubts about the economics profession. I'm not talking about the inability of most people to understand statistics or the counter-intuitiveness of some results of economic analysis. I'm talking about examples like this where economists get too clever and lose the thread of common sense.

That is, it's clear that both points of view are correct: your vote is statistically unimportant but if you place a value on the outcome then your vote has meaning in that context. Ordinary people have understood this forever. They might not get the math but they understand this basic stuff.

A pro-life voter, for example, might place an extraordinary value on the outcome of an election. Even the smallest impact of that single vote carries tremendous weight for that person and for the pro-life community. I did not read the linked article, but I assume it addresses how these weightings are explicitly used to generate votes.


Lyn Lejeune

Let's see: voting, you mean my vote counts after all? Isn't that the foundation of our democracy and that little sticker they give us after we come out of the voting both. So, statistics will bear out the fact that one plus more than one and the math changes things in politics, the assumption being the votes are truly counted. Now I voted in the Florida primary and as yet my vote and the vote of millions of other Floridians have been substracted, or is that invalidated, in a holding pattern, just because a bunch of pusses sat around getting their you-know-what's out of gear and we still are subject to the winds of political muscle rather than those numbers. Mathematics of democracy and did you say something about REASON?

Freddy First

The Freakonomics et al approach to voting tends to ignore the benefit of aggregate vote totals. It is true that any one individual vote will have virtually no effect on the outcome in terms of who wins and who loses. However, aggregate totals, both total participation and margin of victory, affect the legitimacy of the outcome. I may not be able to tip the balance between Candidate A and Candidate B, but every vote cast makes the outcome marginally more legitimate and has a marginal effect on the winner's mandate post-election. While these effects get very tiny, each vote does have at least some marginal utility.


i just want to throw out my old chestnut again: any examination of the rationality of voting which doesn't take into account the relative vaule of the possible outcomes is intrinsically flawed. however low the probabilty of effecting the outcome, there exists some value for which the benefit of voting outweighs the costs, and voting becomes rational.


Unfortunately, kind people are not noticeably more intelligent than selfish people. So we get good effort, bad execution, you know?

Chris Blattman

My reading of the paper is that the results and findings are driven by inter-election variation. That means, everyone still has identical preferences altruistic preferences within an election.

I think that means to explain variation in turnout within countries, we have to assume that how much you care about people changes over time, unless all of th action is in changes on the payoffs. To explain turnout across countries you have to assume people in different countries have different altruistic preferences.

This raises the question: why might altruism change across time and place? Do we really think that the fluctuations in US turnout are driven by differences in just payoffs and altruistic preferences over time?

The trouble with the predictions of the model is that the authors don't state what the predictions of an alternative model would be. The leading contender, in my mind, is that people gain some utility from the act of voting itself. The theory and evidence around this are only weakly developed. testing between competing hypotheses seems to me to be the only way ahead here.



Not only does Australia punish you for not voting, their voting system removes the voter's paradox. On their ballots, you rank the candidates 1-6. Whomever gets the lowest number of #1 votes is out and everyone who voted for them immediately has now voted for their 2nd choice. This process repeats until only 1 person is left.

Imagine it. Being able to vote for Nader without worrying that your vote hurts the Democrat's candidate or vice versa with Pat Buchanan and the Republican's candidate. We would no longer have to hear people whine about how McCain isn't conservative enough or how 3rd party candidates aren't given enough press coverage. And just perhaps, this system would encourage people enough to raise the number of people who vote without having to resort to punishing those who don't vote.


I suspect that there needs to be more work done on the maths models to get around this kind of conclusion. Because it is clear that a large number of votes counts, and it is clear that a large number of votes is made up of individual votes. So an individual vote must count.
The current models seems to say 'no single person should vote, it doesn't make a difference'. However IF no single person voted, it WOULD make a difference!

Maybe the problem with the equation is the perceived 'cost' of voting. Once every 4 years going to a convenient location is not a huge cost. It is a very tiny cost.

ba, thats enough, you get the point.