Monday, September 27, 2004

No Poll-Box Paradox

Chris Bertram of Crooked Timber raises an objection to the notion of rational non-voting (the idea that people don’t vote because the miniscule expected benefits are swamped by the costs):
What’s wrong with this argument? Well, one thought, which I remember hearing first from my friend Alan Carling, is this: the argument involves inconsistent assumptions about rationality. The assignment of a low probability to my vote making a difference assumes what the conclusion of the argument denies, namely, that rational persons would vote. But the argument says they wouldn’t. Well if they wouldn’t then I would be the only voter (a dictator, in effect). In which case I would certainly be rational to vote since I can count the full expected benefit of $1000 in favour of doing so. But if that’s the case, and I should vote, then so should everyone else … in which case I shouldn’t … in which case nor should they … in which case I should ….
It sounds like a paradox, but really it’s not. I play on the seeming paradox when I say to my students, “For economists, the question is not why people don’t vote; it’s why they ever do!” But even that question is not terribly difficult to answer.

First, “rational” is not synonymous with “self-interested” or “materialistic” or “concerned only with outcomes.” It simply means acting consistently with one’s own preferences, whatever they might be. There is nothing irrational about voting because (a) one feels a civic or moral obligation to do so, or (b) one derives some kind of direct pleasure from the expressive act. And indeed, that is probably a sizable chunk of why most people vote. Some people entertain the myth that “every vote makes a difference,” but most will admit – at least upon prodding – that their one vote will almost certainly not alter the outcome of the election. They continue to vote because they derive some kind of direct psychic benefit from voting (or perhaps a psychic cost from shirking).

But second, even if we assume people are solely concerned with their votes’ effects on electoral outcomes, no paradox arises. The reason is that the expected benefits of voting decrease as the number of voters rises. If no one else were going to vote, your vote would be decisive. If ten other people planned to vote, it would still make sense to cast a ballot. Even if a hundred or a thousand other people intended to vote, it would not be outrageous to think your vote could stand a chance of making a difference. When the number of other voters numbers in the millions, of course, the expected benefit is vanishingly small. The rational non-voting argument, like most economic arguments, is a claim about the marginal chooser – in this case, the voter right on the cusp between voting and non-voting. Since the marginal benefit of voting declines with the number of voters, there is a turning point at which the marginal benefit sinks below the cost. For the marginal voter, the expected benefit should be approximately equal to the marginal cost.

The two arguments work best in concert. The rationality of voting when few others will vote assures that at least a certain number will vote. Feelings of civic duty and self-expression pump up the marginal benefits further. Together, these factors assure a large enough voting public to make the probability of your vote affecting the outcome tiny relative to the material costs. Only if your psychic benefit of voting is large enough to cover this rather sizable gap will you choose to vote.

Chris’s objection can be rejuvenated by observing that while it’s rational for some people to vote, the model does not determine which people will vote. Suppose, for instance, that the marginal voter’s expected benefit of voting – including all psychic benefits – dips below the cost when the number of other voters reaches (say) 10,000, in an overall population of 100,000. There is still a question of which 10,000 voters will vote. Why these 10,000 people instead of those 10,000 people? The problem has multiple equilibria, and there’s no obvious means of determining which equilibrium will in fact occur (a common feature of economic models that produce multiple equilibria). But the most plausible argument (to me, at least) is that the voting contingent will consist of those voters with the highest psychic benefits, which are independent of the number other voters.

To recapitulate: The rational non-voting theory is a theory of the marginal voter. It is fully consistent with the existence of a situation in which some people vote and others don’t, even if people assess the benefits of voting purely based on its electoral effects. However, recognizing the existence of benefits derived from the act of voting itself allows for a more complete explanation of (a) why as many people vote as do and (b) which people do in fact vote.

UPDATE: I originally attributed the CT post to Henry Farrell, an error I've now corrected.


igbrooks said...

I’ve seen this argument a number of times on economics blogs, but it’s never quite sat right with me. An important function of elections seems to have been overlooked.

Voting ratifies the political process. If only 10% of the eligible population votes, the authority of the government is diminished. A lame-duck legislature known to enjoy very little popular support will be unable to enact sweeping legislation, and also will be less able to enforce the law. If 20% of the population is known to smoke marijuana, say, in violation of the law, can such a government rightly take police action against them? (True, if this group became energized single-issue voters, one might expect that the law would change after the next election, but this constituency is notoriously disaffected). Perhaps a libertarian would not be displeased by governmental impotence, but it seems that even a minimal state cannot function without popular support. Governments perform better and are felt to be less oppressive when they are seen to be widely supported, boons shared by all citizens. This expected benefit of voting does not decrease as the number of voters rises. (or at least, does not decrease to zero – moving from 10% to 20% will have a far greater positive effect than moving from 80% to 90%. Even so, it will decline far more slowly than the power of a vote to influence an election’s outcome)

I think this explains why many people understand voting as a civic duty. A utilitarian, altruistically seeing their own interests as no more important than those of other individuals, will vote when voting increases net utility for all citizens, and will do so even if the effect on their own net utility is negative. People feel good about voting because they think they’ve done something good for others at their own expense.

By this logic, non-voters are free riders on the benefits provided by stable and legitimate government. Mandatory voting does not eliminate the free rider problem, since forcing someone to the ballot box does not demonstrate their support for the political process. People being what they are, many citizens will choose not to vote in free elections, since the marginal utility of voting for them may well be negative, if enough other people vote to validate the electoral process.

When we cannot (directly) provide incentives for behavior that benefits all society, we make moral appeals. So VOTE, not because it’s good for you, but because it’s good for everyone.

Glen Whitman said...

Igbrooks -- are we disagreeing? The theory of rational (non-)voting is a positive claim, not a normative one. It claims that some people will choose not to vote because the marginal costs (as they perceive them) exceed the marginal benefits (as they perceive them). If the social benefits exceed the private benefits, as you claim, then there is a positive externality or public good problem that leads to inefficiently low voting turnout. Inculcation of moral/civic norms is one means of dealing with collective actions; it works by getting people to internalize some of the benefits or costs of their actions to others. I argued something very like this in a previous post:

However, given a context in which both major parties regularly push illiberal agendas, I have no particular reason to care about the specific social "benefit" you cite -- the legitimacy of government. I think there is more social benefit to casting doubt on the government's legitimacy by voting for a third party candidate.

The Genius said...

If you look at voting records more people vote in elections involving presidents than in elections involving strictly local candidates. This would seem to be counter intuitive since there is no chance one vote will make a difference in a presidential contest while there is a small chance that one vote will make a difference in a local election. That seems to indicate that people do not vote because they expect their vote to make a difference, but for other reasons. One reason is probably the good feeling they get from doing their duty. Another, and I think the biggest reason, is to identify themselves with the candidate and/or party they think of as being right. This is similar to rooting for one's favorite golfer or race car driver. The voter then acquires the satisfaction of being a part of a winning team if their candidate wins or a sense of superiority to the masses if their candidate loses. I have voted in every national election since I turned 18 and will continue to do so. The satisfaction and feel every time I see the President and guilty pleasure I feel when I read about what Al Gore is doing is worth much more to me than the small amount of effort it took to vote.

igbrooks said...

Thank you for your reply, Glenn. You're right -- there is no disagreement between us on the theory of rational non-voting seen as a positive claim. We also agree that moral norms can rightly be used to ameliorate problems of public goods.

It was my intention to argue that voting increases the legitimacy, not of the winning party, but of the political system. Government does not exist without the capabillity to pass and enforce legislation, and the power to prevent other groups from doing so. In my view, a government is legitimate to the degree that it can obtain these powers by the free consent of its people. A voter by voting explicitly consents to be governed by those elected by the majority. Non-voters have given only implicit consent. They haven't gone into exile, but perhaps they're deeply discontented -- angry enough to support a junta, even. A democratic state can be strong and stable only if most people are seen to consent to the method by which we resolve policy disputes.

Well and good so far. Here's where I made a rather silly mistake in my previous post. Following the theory of rational voting, voter turnout is a(n imperfect) measure of the commitment people have to their institutions. Keeping in mind the negligible marginal effect of a single vote on an election's outcome and holding constant the pleasures of self expression, increased voter turnout reflects increased feelings of civic duty. (assuming there are no other motivators) But it is increasing commitment to government , not increasing voter turnout, that will improve the state's abillity to provide public goods. Perhaps increased explicit consent to government makes for government more just as an abstraction of political theory, but it is unlikely to make a practical difference in people's lives.

Of course, even libertarians ought to be strongly committed to the political process, as indeed you argued in your older post ("A Libertarian Case Against Non-Voting," Thursday, August 05, 2004)

Of course, if we did want to increase voter turnout, methods other than moral norms are availiable. Many have proposed that the American government should make election day a national holiday, reducing the marginal cost of voting. For that matter, in Athens in days of yore, they used to pay people to vote, did they not?

As for third party voting...well, as a Canadian citizen I had four serious candidates and a host of fringe choices (even Marxist-Leninist!) to choose from last time I voted federally. I think that voting for a candidate who has little or no chance of being elected is a viable strategy. If enough people do so, one of the major parties may shift their platform to reassimilate them. At the very least, you register discontent with the availiable options. Even in doing so, you say that you are willing to work within the system to see changes made (rather than building barricades in the street, say).