There’s an article by Stephen Dubner and Steven Levitt in the New York Times today on why it’s rational to vote. They correctly point out that the probability of casting a decisive vote is very small. Unfortunately they don’t seem to be aware of the social-benefit motivation for voting, which is why voting is, in fact, rational behavior. See here for our paper on the topic. For convenience, I’ll repeat our earlier blog entry below. The short version is that you can be rational without being selfish.
The chance that your vote will be decisive in the Presidential election is, at best, about 1 in 10 million. So why vote?
Schematic cost-benefit analysis
To express formally the decision of whether to vote:
U = p*B – C, where
U = the relative utility of going and casting a vote
p = probability that, by voting, you will change the election outcome
B = the benefit you would feel from your candidate winning (compared to the other candidate winning)
C = the net cost of voting
The trouble is, if p is 1 in 10 million, then for any reasonable value of B, the product p*B is essentially zero (for example, even if B is as high as $10000, p*B is 1/10 of one cent), and this gives no reason to vote.
The usual explanation
Actually, though, about half the people vote. The simplest utility-theory explanation is that the net cost C is negative for these people–that is, the joy of voting (or the satisfying feeling of performing a civic duty) outweighs the cost in time of going out of your way to cast a vote.
The “civic duty” rationale for voting fails to explain why voter turnout is higher in close elections and in important elections, and it fails to explain why citizens give small-dollar campaign contributions to national candidates. If you give Bush or Kerry $25, it’s not because you’re expecting a favor in return, it’s because you want to increase your guy’s chance of winning the election. Similarly, the argument of “it’s important to vote, because your vote might make a difference” ultimately comes down to that number p, the probability that your vote will, in fact, be decisive.
Our preferred explanation
We understand voting as a rational act, given that a voter is voting to benefit not just himself or herself, but also the country (or the world) at large. (This “social” motivation is in fact consistent with opinion polls, which find, for example, that voting decisions are better predicted by views on the economy as a whole than by personal financial situations.)
In the equation above, B represents my gain in utility by having my preferred candidate win. If I think that Bush (or Kerry) will benefit the country as a whole, then my view of the total benefit from that candidate winning is some huge number, proportional to the population of the U.S. To put it (crudely) in monetary terms, if my candidate’s winning is equivalent to an average $100 for each person (not so unreasonable given the stakes in the election), then B is about $30 billion. Even if I discount that by a factor of 100 (on the theory that I care less about others than myself), we’re still talking $300 million, which when multiplied by p=1/(10 million) is a reasonable $30.
Some empirical evidence
As noted above, voter turnout is higher in close elections and important elections. These findings are consistent with the idea that it makes more sense to vote when your vote is more likely to make a difference, and when the outcome is more important.
As we go from local, to state, to national elections, the size of the electorate increases, and thus the probability decreases of your vote being decisive, but voter turnout does not decrease. This makes sense in our explanation because national elections affect more people, thus the potential benefit B is multiplied by a larger number, canceling out the corresponding decrease in the probability p.
People often vote strategically when they can (in multicandidate races, not wanting to “waste” their votes on candidates who don’t seem to have a chance of winning). Not everyone votes strategically, but the fact that many people do is evidence that they are voting to make a difference, not just to scratch an itch or satisfy a civic duty.
As noted above, people actually say they are voting for social reasons. For example, in the 2001 British Election Study, only 25% of respondents thought of political activity as a good way to get “benefits for me and my family” whereas 66% thought it a good way to obtain “benefits for groups that people care about like pensioners and the disabled.”
Implications for voting
First, it can be rational to vote with the goal of making a difference in the election outcome (not simply because you enjoy the act of voting or would feel bad if you didn’t vote). If you choose not to vote, you are giving up this small but nonzero chance to make a huge difference.
Second, if you do vote, it is rational to prefer the candidate who will help the country as a whole. Rationality, in this case, is distinct from selfishness.