In the aftermath of linking to my article with Aaron and Nate about the probability of your vote being decisive, Conor Clarke writes:
If your decision to vote is motivated by the sense that “one vote can make a difference,” you are being substantially less rational than someone who never leaves the house for fear of being killed by a meteor. Voting is irrational.
I completely disagree with this last statement, and I know that Aaron does also. Here’s we wrote on pages 4-5 of our article:
A probability of 1 in 10 million is tiny but, as discussed by Edlin, Gelman, and Kaplan (2007), can provide a rational reason for voting; in this perspective, a vote is like a lottery ticket with a 1 in 10 million chance of winning, but the payoff is the chance to change national policy and improve (one hopes) the lives of hundreds of millions, compared to the alternative if the other candidate were to win. Different voters have different opinions about which candidate is desirable, but many can feel that their preference is not only better for them personally but for millions of others.
Aaron and I (with Noah Kaplan) discuss the rationality of voting in more detail here and here.
The key issue
In one of his posts, Clarke write, “we don’t vote for our ‘rational’ individual benefit. Clarke’s mistake (from our perspective) was to glue “individual benefit” on to “rational.” I would define rational as reasonable, purposeful behavior, not required to be self-interested at all.
More on the topic here, in a discussion of a John Quiggin paper from 1987 and a Dale Miller paper from 1999.
Summary
I think that Aaron and I agree with Clarke on the substance: people vote for good reasons having to do with their views of what’s best for the country and the world. Aaron and I argue that voting is one reasonable way to affect the direction of policy: it’s a low-cost activity with a very small chance of a very huge benefit–not to oneself but to the general population. I think we’re just disagreeing with Clarke about the use of the word “rational.”
P.S. On the other hand, for voters in states such as New York, California, and Texas where the probability of a decisive vote is closer to 1 in a billion, any reasons for voting must go beyond the any instrumental rationality. So I’m certainly not arguing that voters are always rational.
Voting is like a giant cooperative n-player game. It's like an n-player version of the Prisoner's Dilemma. It is strictly rational in game theory terms for each prisoner to defect against the other. No matter what one prisoner does, the other prisoner is better off defecting. To defect is the dominant strategy, which is like staying home instead of voting.
Despite being "irrational," if the prisoner's have faith in one another, they are both better off in the long run by cooperating. This is learned and reinforced through repetition of the game.
It's no different than any other civic duty. It does not immediately serve one's self-interest, and it has to be taught and reinforced.
"I would define rational as reasonable, purposeful behavior, not required to be self-interested at all."
Why would you define rational that way? The definition seems obscurantist to me.
Brian: Voting is different from a prisoner's dilemma. Even if millions of others are voting, it can be rational for you to vote. On page 298 of our article, Aaron, Noah, and I derive the feedback mechanism that explains why, without any collusion among the voters, it is not a dominant strategy not to vote.
Hopefully: Rational = doing something based on reason. My definition is pretty much derived from the dictionary definition.
Professor Gelman,
If I understand you correctly, after skimming your paper and this post, your main claim is that it's rational for a person to vote in a typical state, if they're voting for a 1 in 10 million chance to affect the lives of 300 million people. That activitty is rational because it's "reasonable, purposeful, behavior", "doing something based on reason".
What's the importance of the numbers to this argument? It feels to me like a fuzzy and obscure argument, leaning heavy on the aesthetics of the majority, is being draped with some numbers that have a poorly articulated connection to the argument.
Where's the magic numerical point where a % of chance to affect an election outcome becomes rational, besides a cost-benefit analysis for algorithmic self-perpetuation by the voter (what I think is implicit but a bit obscured by the term "self-interest"?)
I think it all becomes arbitrary or obscured primate aesthetics once one moves beyond maximizing algorithmic self-perpetuation odds for the determination of rational behavior.
Why is it not rational to vote to exercise 1 in 100 billion chance to affect the lives of 1 million people by your definition?
The math is interesting to me, but your definitions seem to me to be needlessly murky.
Still, it is useful to look at odds of an individual action in a mass activity causing a particular result.
Feel free to edit this comment if it's too long -I'm posting the unedited version on my blog.
My vote, togethger with my fiancee's and my parents, literally swung a local election two years ago — 2-vote margin.
It was blatantly rational to vote.
The definition seems tautological. Is it meant to suggest that if you have some reason for what you do, any reason of any quality, it qualifies as rational? I am not sure how low the bar is meant to go.
I think the definitional argument you want, phrased in a manner that appeals to people who assume "self-interested," is to focus on "value-maximizing" or something similar. Even the most self-interested person can value others' welfare, want a culture that embodies his/her values, etc. If Ayn Rand says that rational selfishness can include caring about others' welfare, you will not find more extreme arguments about self-interest out there. Yes, I really think it is just a matter of saying the magic words, "I value others' welfare," maybe toss in something about your utility function.
On the other hand, there are many who really do not care. Their values may include the welfare of their friends and family, or some larger group, but the other 6 billion people they will never meet carry no personal value to the speaker. I don't suppose that you need to be a complete sociopath to say that, for someone who you will never know if he lived or died, you do not care if he lives or dies. For those people, no, benefit to 300 million other Americans probably holds little to no weight. For them, voting will remain irrational, although they may accept that it would be rational for you given your values (to the extent that they accept that you can rationally value all those people you will never meet0.
From my limited understanding of game theory, I think some there is likely a clash of terminology. In game theory, an agent is self-interested if she has her own mapping from outcomes to utilities and says nothing about whether that mapping reflects any specific personality traits. Such a mapping could be entirely unselfish, for example. In this sense, being rational implies nothing other than acting reasonably and purposefully given one's own preferences over outcomes.
With respect to voting, I think it's very difficult to make any sweeping statements about rationality based on a simplified perspective of the game. For example, regardless of who wins, each correctly cast vote will be counted and will show up in results. As such, some utility could be derived by having one's vote contribute to a public tally. Even though its a very coarse method of communication, voting is an important way of letting politicians know what types of issues win your vote. In Canada, each vote for a party in a federal election means the party receives some extra public money (I think it's around $2) for campaigning in the next election so there is even more incentive to vote.
It's true that if all you're interested in is the short-term outcome of an election, you can probably stay at home but that is not usually the extent of one's interest.
the payoff is the chance to change national policy and improve (one hopes) the lives of hundreds of millions
People could have the altruism of their vote benefiting the lives of milions in mind, or they could have what Amartya Sen refers to as "nosy" preferences. My vote has the 1 in ten million chance of improving the utility of the millions of people who are like me, AND a 1 in ten million chance of subjecting my group's preferences onto the uncivilized mob that disagrees with me… Your optimism is commendable, if not heroic though….
People almost never question the rationality of voting without making a big assumption, namely, that people only care about the effect of their vote would have if it is decisive.
This assumption is essentially built in to the definition of rationality that is used. Andrew, Aaron & Nate, carefully show that even under this assumption, (or equivalently, this definition of rationality) voting can be rational.
With other, equally good definitions of rationality, the question would never be raised. Personally, I enjoy participating in the democratic process through exercising my right to vote and the opportunity cost of voting is small – therefore it is rational for me to vote. Isn't that a useful way to think about it?
I suspect people questioning the rationality of voting have at least one of two motivations. 1) to encourage people to think about the actual effect of their vote, and what their true motivation for voting is, or should be.
2) to signal that they are a clever and independent thinker, unafraid to challenge conventional wisdom.
Are you arguing that non-voters are always irrational? If no, then is their choice ever irrational?
In any event, I think voting is best (but of course not fully) explained by signalling, and arguments about "rationality" often become useless because unfortunately no one can ever agree on a definition.
"P.S. On the other hand, for voters in states such as New York, California, and Texas where the probability of a decisive vote is closer to 1 in a billion, any reasons for voting must go beyond the any instrumental rationality. So I'm certainly not arguing that voters are always rational. "
You could give a few different stories here:
(1) Rule-based utilitarianism works fine – even if California and Texas are solidly Blue/Red now, that might change, so, if you make a once-for all choice, voting makes sense
(2) Concern with size of majority
(3) Bundled goods. It costs no more in US elections to vote for the whole party ticket than for a single candidate who might have a chance
(4) Support for the electoral process (and high turnout) as a public good