During the 2010 gubernatorial elections, we elicit voter beliefs about the closeness of the election before and after showing different polls, which, depending on treatment, indicate a close or not-close race. Subjects update their beliefs in response to polls, but overestimate the probability of a very close election. However, turnout is unaffected by beliefs about election closeness. A follow-up RCT, conducted during the 2014 gubernatorial elections at much larger scale, also points to little relationship between poll information about closeness and turnout. We caveat that the strength of our evidence depends on assumptions regarding our treatments' impacts on beliefs.
Gerber, Alan, Mitchell Hoffman, John Morgan, and Collin Raymond.
"One in a Million: Field Experiments on Perceived Closeness of the Election and Voter Turnout."
American Economic Journal: Applied Economics,
Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior