For about 20 percent of voters, the probability of voting is related to the likelihood that their vote will be pivotal, which depends on election size and expected closeness of the election.
Why do people vote in elections with many participants, even if their vote may not be pivotal? In Rational Choice and Voter Turnout: Evidence from Union Representation Elections (NBER Working Paper No. 16160), Henry Farber studies over 75,000 union representation elections held from 1972-2009 in the United States to try to address that question.
These government supervised, secret-ballot elections on the question of whether the workers would like to be represented by a union, generally held at the workplace, provide a good way to study voter behavior: many of them have few enough eligible voters that individuals can reasonably expect that their votes may be pivotal. Farber finds that in a typical union representation election, over 80 percent of individuals vote without any consideration of whether their vote will be pivotal. However, for about 20 percent of voters the probability of voting is related to the likelihood that their vote will be pivotal, which depends on election size and the expected closeness of the election.
Farber's finding suggests that the behavior of a substantial group of voters, but still a minority, is consistent with the standard rational choice model. This model recognizes that when voting is costly, individuals will consider the consequences of the various electoral outcomes and the probability that their vote will be pivotal in deciding whether or not to vote. In large elections, the likelihood that an individual's vote will be pivotal is so small as to make it unlikely that the expected benefit of voting will outweigh the costs. Thus the rational choice model predicts lower turnout rates in larger elections and higher turnout rates in elections where preferences are relatively evenly split.
Farber admits that there are limits to how far the lessons learned by studying turnout in NLRB representation elections can be generalized to larger political elections. First, even relatively small local elections are much larger than most elections in his study. Second, the physical cost of voting in political elections is higher, because the elections generally are held at a location to which the voter must travel, while NLRB representation elections are held in the workplace. Finally, for an individual the stakes in a political election are generally lower than in an election that can fundamentally alter the employment situation. All of these factors likely contribute to the higher turnout observed in NLRB representation elections.
-- Lester Picker