In this election season, the conventional wisdom says that Americans should vote. Indeed, this message is pounded into our heads through overwhelming repetition. But those spreading this message often cast into doubt their own case by making such arguments as the this, from a public service announcement: "it doesn't matter how you vote, just that you vote". But if it doesn't matter how we vote, why bother?
There is, however, a counterpoint to the conventional wisdom that holds that voting is basically irrational. This argument begins with the observation that the chances of any one person's vote changing the outcome of a major election (president, congress, statewide office) is infinitesimal. Someone did the math and concluded that you are more likely to die in a car crash on the way to the polls than to change the outcome of an election. Since your expected outcome is negative, the argument concludes that it is irrational to vote. This has become something close to conventional wisdom amongst economists.
One critique of this argument points out that it is only true on the margin. That is, it assumes that lots of other people are already voting. The fact that there are so many people voting is the reason why your vote is so unlikely to sway the outcome. If everyone followed the advice of this argument and stayed home, then nobody would vote. But if nobody voted, then casting a single vote would decide the outcome of every race.
Others point out some of the reasons why people vote. People may vote because they enjoy voting, or because they feel it is their 'civic duty', or because they would feel guilty about not voting. Others may believe that their vote is likely to change the election results. But none of these explanations address whether voting is rational.
Yet it is. The real flaw in the argument against voting is that it is confused about the purpose of voting. It addresses someone's ability to determine who occupies an office. But most voters don't vote simply because they want a particular person to occupy an office (though that may be a factor) but because they hope to affect public policy.
Certainly who wins elections affects public policy. But it is not the only factor. Consider the following thought experiment. In election outcome #1, candidate A wins 99% of the vote to candidate B's 1%, even after a vigorous campaign. In election outcome #2, candidate A wins 51% of the vote to candidate B's 49%.
On the question of who wins the election, these two outcomes are identical. But they do not have equal outcomes on public policy. That is because the actions of elected officials are not predetermined. They are affected by public opinion, which is expressed (among other places) at the polls.
In outcome #1, candidate A is likely think something like "The people love me. I can feel free to pursue my platform with their full support. I can do almost anything within reason and still get reelected." However, in outcome #2, candidate A is likely to think something like "Almost half the voters did not want me to win the election. I have to be very careful about pursuing my platform. I may have to amend or abandon parts of it. If I misstep I may be voted out of office."
While most politicians are not perfectly pliable, neither are they perfectly rigid in their positions. The one exception on the federal level is Ron Paul. Politicians who refuse to respond to public demand generally don't get elected or reelected. Even politicians with deeply-held beliefs rationalize voting against their own beliefs as "recognizing political reality".
Even if a politician is perfectly principled in his votes, he can still respond to public opinion in what bills he introduces and what causes he champions.
The effects of public opinion change on the margin. That is, one additional person supporting a cause changes the actions of politicians. The amount of change may be quite small, of course, in a large electorate. But it is greater than zero. This contrasts with the question of who holds an office, which does not change on the margin. Switching one vote does not shift a little bit of an office from one candidate to another. Your vote either swings the whole thing or does nothing.
Ironically, the case for voting is weakest regarding referenda, since ballot propositions do not respond to public opinion. Yet even here, the margin of victory or defeat can affect future attempts to pass referenda or other legislation.
Thus the conventional wisdom is right, if not for the right reason. Voting is rational, after all.