One in a Million: A Field Experiment on Belief Formation and Pivotal Voting∗

Instrumental voting models predict that turnout depends on the chance of casting a pivotal vote, which is typically extremely low in large elections. Evidence from psychology and behavioral economics suggests that misperceptions of extremely unlikely events are common and subject to systematic biases, sometimes called the non-belief in the law of large numbers. We provide a model of voting when voters suffer from these biases and show that they inflate the perceived pivot probabilities, and hence turnout. Moreover, voters do not fully account for new information of pivot probabilities in this model. We then test the model in a large-scale field experiment during the 2010 U.S. gubernatorial elections where we elicited voter beliefs about a very close election before and after showing different polls. We find that voters massively inflate pivot probabilities and this inflation is most pronounced among subjects measured to have the highest non-belief in the law of large numbers. Furthermore, subjects respond to but fail to fully incorporate new information presented in the experiment. However, the decision to vote is not affected by beliefs about pivotality. Even in a controlled setting and in response to an experimental manipulation that significantly changed the perceived probability of being pivotal, voting behavior is unaffected.