Knowledge and the Rationality of Voting:

Co-Conspirator Eric Posner challenges my argument that it might be rational to vote. He argues that there is little reason to do so because, in the unlikely event that your vote really will break a tie, that probably means that the two candidates were of virtually equal quality:

[B]reaking a tie is beneficial only if your vote is more likely correct than not—that is, you actually vote for the better candidate. Surely your vote is more likely to be correct than not? After all, you have some information, and that means you are doing better than flipping a coin. However, you need to reflect on your own ignorance with some humility. If, by hypothesis, your vote breaks a tie, then it means that (putting aside the vagaries of the electoral system) half the country prefers one candidate and the other half prefers the other. If all of these people have enough information that their votes are not random, the existence of a tie (aside from your vote) indicates that the two candidates are almost exactly equal in quality. The probability that your own puny knowledge (elsewhere in the same article Ilya discusses the problem of rational ignorance—people have weak incentives to inform themselves about the candidates and policy in general) will distinguish the infinitesimally better candidate is itself infinitesimal.

The problem with Eric's argument is the assumption that if the other people's votes are not random, that necessarily means that they are - on average - well-informed, or at least more likely to be correct than mistaken. However, lots of research, such as Bryan Caplan's recent book, and my own article that Eric links to, suggests that voters often make systematic errors where "mistaken" votes for one side are not offset by an equal number of mistakes favoring the other. Thus, if your fellow citizens are equally divided in their voting preferences and are voting nonrandomly, that doesn't necessarily mean that the two candidates are nearly identical in quality. It could be that the weaker of the two is benefiting from systematic flaws in voters' evaluation of the information they have. So my argument for voting in cases where you think there is a big difference in quality between the two candidates still holds true.

Obviously, Eric is right to counsel "humility" in assessing one's own ignorance. If your knowledge is much less than that of the average voter, that may be a consideration in favor of staying home. But if it is equal or greater, then you have a good case for casting a vote if you think there is a substantial difference in quality between the available alternatives. That is especially true once you consider the possibility that you might have underestimated the quality difference in favor of your preferred candidate, a scenario that to some degree counterbalances the chance that you have overestimated.

The reason to vote in an election, despite the personal investment of time and low probability of making a difference, is not the ex ante value of the value of the difference multiplied by the probability of casting a tie-breaking vote.

The reason to vote in an election is to participate in our democracy, and as an entry point to greater participation. Those who vote are further motivated to take additional actions such as communicating with their legislators, serving on citizen advisory councils, or taking additional actions where the probability of making a difference is far greater than in a mere election. Those who fail to vote are disempowering themselves and adding an additional psychological barrier to overcome before they are likely to to participate in our democracy at a deeper level.

Don't underestimate the power of a citizen to move the country. Representative Al Gore held hearings on Love Canal that ultimately led to the passage of significant legislation because a high school student drew his attention to the issue. (Unfortunately, the media, including the so-called liberal New York Times and Washington Post bollixed Senator Gore's remarks on this topic, changing his statement "that [Love Canal] was the one that started it all" to "I was the one that started it all," making Al Gore's story about the high school girl's participation in democracy sound like Al Gore was patting himself on the back.)
10.31.2008 3:58pm
Clarification: Gore's remarks about the Congressional hearings he held on Love Canal, and said "that was the one that started it all," were actually made when he was vice president and running for president, not when he was a senator.
10.31.2008 4:04pm
Henry Bramlet (mail):
Beyond that, who is to say that one candidate is more "Correct" than the other?

The fact is that some candidates will be more beneficial to others. If you chose a candidate because he is more beneficial to you (maybe he won't raise your taxes, or maybe he'll help your local economy more) it doesn't matter that maybe another bunch of people in the country disagree with your preferences.

This strengthens Ilya's point. If we were just talking about whether or not your tie-breaking vote would pick the "best" candidate, then Eric's point might have weight. But we are talking about whether or not your vote will pick the best candidate for YOU. In that case, your vote is very important, as it could mean choosing your candidate rather than the best candidate for your arch enemy.
10.31.2008 4:10pm
This is somewhat analagous to the paradox of efficient markets:

If markets were perfectly efficient (prices incorporated all possible information), then there would be no incentive for people to collect information in order to make good investment decisions.

But... as soon as there was a disincentive to collect information, the market would cease to be efficient on some level, and some investors would have an incentive to go out and get that information and make buy/sell decisions based on it.
10.31.2008 4:39pm
Suzy (mail):
On Eric's view, does the better candidate always win, then?
10.31.2008 4:48pm
frankcross (mail):
I can't understand how equal knowledge would counsel for voting.

But of course the problem comes down to humility. Who is deciding whether you have "equal or greater" knowledge. Presumably the voting person. Yet we know that people's self-assessments on these matters are vastly inflated.

I think eyesay is right, the reason to vote is if you get utility from voting.
10.31.2008 5:03pm
Obvious (mail):
Frank Cross: "I think eyesay is right, the reason to vote is if you get utility from voting."

In this conception, one votes for the same reason one enjoys recreational sex or drugs. It adds some value to one's life. One enjoys doing it.

It might still be the case, of course, that nonetheless, the morally proper position is abstinence. It might still be correct to Just Say No...
10.31.2008 6:06pm
I think the calculation of the probability your vote will swing the election may be based on a false assumption. Except in the case that your vote is the one and only vote cast, your vote can never swing the election. Your vote is only one of many that swings the election. So even if your vote is one of 60 million against 40 million, your vote contributed one 60 millionth to electing the correct candidate.

Maybe we should think of voting as a tax paid in labor that we must contribute to maintain our democracy. If all you care about is yourself then you can avoid the voting tax, but if you care about humanity, and if it looks like the wrong candidate might get elected, then maybe you should put in your vote and make your tiny contribution, even if it looks like your vote is very unlikely to swing the election. And even if your vote is in the minority it may encourage more candidates and more contributions and more voters in the future. It's not a question of IF your vote will make a difference, it WILL. It will make a small contribution.
10.31.2008 6:57pm
I'm surprised we're even seriously discussing whether it's 'rational' to vote. Maybe next we'll discuss whether it's 'rational' to counterfeit money?

One should cast an informed vote because it is one's civic duty in a democracy. The effects of a single person failing to vote are tiny, but if no one votes, then our system of government would break down [or break down even further than it already has]. Likewise, a single person counterfeiting a small amount of money would have little effect on our financial system. But if large numbers of people engage in counterfeiting, then our money would become worthless and our financial system would break down.
10.31.2008 7:07pm
I think timd is on the right track. The answer has to do with the way markets aggregate data - the process has a value separate from the value of any individual data point.
10.31.2008 7:21pm
guest 2L:
I'm not sure whether this has been gone over in previous posts, but the original argument in Ilya's article seems somewhat suspect. He seems to be accepting the following "rational" calculation of the utility of voting:

(value of changing the outcome) * (probability that your vote changes the outcome) - (the cost of voting (Cv) = (the utility of voting (Uv))

But then he argues against those who suggest that such a calculation would make voting irrational. The probability that your vote changes the outcome might be miniscule, but the value of voting might very large. In particular, if you care about each and every one of your fellow citizens just 1000th as much as you care about yourself, then the calculation would look like:

D*(300 million/1000)/(100 million) -- Cv = Uv

(D is the expected monetary benefit per voter. The probability is assumed to one in 100,000,000 that your vote changes the outcome. I would think the formula should be D*(1+ (300 million/1000))/(100 million) -- Cv = Uv, but that's not a big issue.)

The problem I have with this argument is that it seems to mask the underlying assumption that the value to the voter of changing the election is D*(300 million/1000). Ilya assigns a value of $5,000 to D. Fair enough, but if you do the math, the value to the voter of changing the outcome of the election is $1,500,000,000. What is that? Would an average voter be willing to pay $1.5 billion to change the outcome of the election? As important as this election might be, I wonder whether Ilya might have overestimated the extent to which the average voter cares about the outcome.
10.31.2008 8:09pm
guest 2L makes a good point, Ilya. To ask 2L's question a bit more directly: Do you really value the difference between McCain and Obama winning at anything remotely approaching 1.5 billion dollars? and if not why not, given your analysis?

I suspect that the answer is that in practice you value a random american's welfare much less than 1/1000th as much as your own.

(btw this observation only gets more forceful if one takes your original analysis seriously and applies it to voters in general - if they are like you then they, like you, will value the McCain/Obama diff at 1.5 billion, which means D should really be set to 1.5 billion not 5000 (ie 300,000 times bigger), which implies a value to you of 300k*1.5billion, and things get very unreal fast).

So I think this analysis needs some work in terms of assumed constants (1/1000 is probably much too big for most folks), structure (to avoid the divergent feedback cycle described above), and scope (in particular, other considerations such as impact on related behaviors, impact of changing the vote count by 1 even if non-decisive, impact of the mere fact of one's voting on others' behavior, etc. may be significant or even dominant factors given typical voter values).

Do you buy any of this?

PS. having keybd problems, pardon the intermittent ee cummings effect..
11.2.2008 1:45am
Jon Roland (mail) (www):
The preceding analyses are deficient in several ways.

First, there are two key questions:
1. Whether to vote.
2. How to vote.

And the utilities of each affect the other.

Second, what we have is a game from the prisoners' dilemma family, and one that is studied in public choice theory.

What is rational for the individual is not rational for the group. In voting the individual voter is cooperating with the strategy that is rational for the group. The penalty for defecting is social disapprobation, and the reward for cooperating is the sense of social bonding to the group, which puts the behavior into the field of behavioral economics rather than classical market economics.

In other words, one votes to do one's duty to defend the group. For most people, dooing one's duty to the group provides a sense of satisfaction that can overcome a certain amount of the costs involved. A society flourishes to the extent that most of its members operates in that way, and fails when the sense of social bonding fails.
11.2.2008 11:07am
Jon Roland (mail) (www):
Another approach to calculating the utility of voting is to base it not on the probability of turning the outcome, which is likely to be very small except under highly unlikely circumstances, but on the effectiveness of "sending a message" to the policy market by making a "purchase" of a candidacy alternative. On this analysis, one is likely to have more influence of policy positions by voting for a minor party candidate in a close election than by voting for a major party candidate. Considered in this way, if the desired direction of a policy shift is away from that of either major party or candidate, then voting for the minor party candidate is the most rational choice.
11.2.2008 5:52pm
dprobins (mail):
I agree that you shouldn't vote if you are less informed than the average voter. But why stop there--shouldn't you decide your vote based on a poll of the most informed voters? Unless you believe that you are the most informed/unbiased person in the world (or that it would be too costly to find a better voter), voting based only on your idea of which candidate is better is suboptimal.

This is not a reductio ad absurdum. It's just scary.
11.2.2008 10:38pm