The rationality of voting

by Neil Rickert

There are a couple of posts at the Becker-Posner blog about voting, and about the reasons that people vote:

Becker expresses the question with

This raises the very old question of why people vote in large elections when their chances of being a pivotal voter are virtually zero, and when voting takes time and is often inconvenient. The electorate is surely conscious of the cost to them of voting since, for example, turnout is usually much smaller when the weather is very bad. The common answer nowadays about this so-called paradox of voting is not that voters are irrational, but rather that they vote for reasons other than to influence outcomes. They may vote to indicate their moral support for particular candidates, or because they believe they express a precious right when they vote, or for other non-instrumental reasons.

In turn, Posner expresses his curiosity with:

The paradox of voting in national elections is that, since a single vote is almost certain to have no effect on the outcome (in a Presidential election, it will merely add one digit to an eight-figure number), there seems to be no benefit from voting. The cost is small enough (if it’s high for a person, he is unlikely to vote), but it’s positive, so that if the benefit of voting is zero the voter is being irrational. Yet, as Becker points out, more than 100 million people bothered to vote in the recent Presidential election.

As it happens, I regularly vote in federal and state elections.  As best I can remember, I have voted in every election since I became eligible.  Yet, at the same time, I am a member of several professional societies, and I rarely vote in the election of officers in those societies.

This raises two questions about me.  Why do I vote (for the cases where I do vote), and why don’t I vote in the other case.  I shall attempt to answer both of those.  I will point out, however, that self-analysis is not alway reliable as a way of determining motives.  So feel free to take my answers with a grain of salt.

Why I vote

I’ll begin with my reasons for voting.  I will center my comments around the recent presidential election, the contest between Barack Obama and Mitt Romney.

According to the analysis of both Becker and Posner, my single vote has very little effect.  As it happens, I vote in Illinois.  And Illinois was widely considered to be a sure win for Obama.  So presumably, my single vote in Illinois has far less significance that would my vote have had if I were voting in Ohio.

Still, I think the analysis is mistaken.  Posner seems to suggest that the benefit of voting is zero.  I see that as clearly mistaken.  To me, it seems to depend on the same sort of mistaken thinking as that involved in the sorites paradoxes.  If everyone who favored my preferred candidate  chose not to vote, then the other candidate would win (unless of course, those voters also chose not to vote).  So there is a statistical significance to my vote.  It accounts for a small part of the overall probabilities involved in deciding the election, and that small probability is greater than zero.

There’s a second problem involved here.  In a probability model, we compute the expected value of the outcome by multiplying the probabilities of individual events by the values of what results with that probability.  As I look at the last presidential election, it seems to me that the world that results from an Obama victory is very different from the world that would likely have resulted from a Romney victory.  And I much prefer the first of those potential outcomes.  So I must multiply the perceived value of an Obama victory by the small probability that my vote will have an effect, in order to determine the value that my vote entails.  It is difficult to give a numeric value to that, but I am inclined to think it large enough to be worth the cost of voting.

There are additional benefits not counted in the analysis suggested by Becker and Posner.  Politicians do look at vote totals.  A president who wins with a strong majority is in a stronger position than a president who barely scrapes up enough votes.  That is to say, he is better able to use the bully pulpit to his advantage.

In practice, I do not attempt those calculations.  I am inclined to think that the model of  the rational economic agent is a flawed model of human behavior.  As I see it, we often rise above the merely rational.

I vote for several reasons.  I see it as a citizen’s responsibility.  And I vote to stand in solidarity with those who support my preferred candidate in states like Ohio, where the election outcome was expected to be very close.  We are, after all, not a collection of individuals but a society of cooperating citizens who work together for our mutual benefit.

Why I do not vote

I often neglect to vote in professional societies to which I belong.  Some of the same reasons for voting still apply.  I do see voting as a responsibility of society membership, much as I see it as a responsibility for citizens.

In order to determine the value of my vote, a similar analysis is needed.  The probability that could be assigned to my vote is small, though probably larger than in elections for the nation’s president.  Yet, to determine the value of my vote, I must multiply that probability by the perceived value of the outcome.  And, in most cases, the perceived value of the outcome is precisely zero.  And that leaves the value of my vote as zero.

The actual value of a particular outcome might well be greater than zero.  But I can only go on perceived value.  I have no way of estimating the actual value.

The problem with most of these professional society elections, is that I am presented with the professional qualifications and vitae of the candidates.  But that does not tell me anything at all about the direction in which they will try to take the society, should they be elected.

In effect, my votes in professional society elections are little more than uninformed guesses.  So I often do not bother to vote.

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