On the Representativeness of Voter Turnout
Prominent theory research on voting uses models in which expected pivotality drives voters’ turnout decisions and hence determines voting outcomes. It is recognized, however, that such work is at odds with Downs’s paradox: in practice, many individuals turn out for reasons unrelated to pivotality, and their votes overwhelm the forces analyzed in pivotality-based models. Accordingly, we examine a complementary model of large-N elections at the opposite end of the spectrum, where pivotality effects vanish and turnout is driven entirely by individuals’ direct costs and benefits from the act of voting itself. Under certain conditions, the level of turnout is irrelevant to representativeness and thus to voting outcomes. Under others, however, “anything is possible”: starting with any given distribution of preferences in the underlying population, there can arise any other distribution of preferences in the turnout set and thus any outcome within the range of the voting mechanism. Particular skews in terms of representativeness are characterized. The introduction of noise in the relationship between underlying preferences and individuals’ direct costs and benefits from voting produces, in the limit, fully representative turnout. To illustrate the potential disconnect between the level of turnout (a focus of much empirical literature) and representativeness, we present a simple example in which, as noise increases, the turnout level monotonically falls yet representativeness monotonically rises.
We thank Stephen Ansolabehere, Thomas Brennan, Anthony Fowler, Ravi Jagadeesan, Benjamin Roth, Matthew Stephenson, and Yufei Zhao for comments; Andrea Lowe, Andrew Paik, John Rady, and especially Jimin He for research assistance; and National Science Foundation grants CCF-1216095 and SES-1459912, the John M. Olin Center for Law, Economics, and Business at Harvard University, the Harvard Milton Fund, and the Ng Fund and the Mathematics in Economics Research Fund of the Harvard Center of Mathematical Sciences and Applications for financial support. Disclaimer: Kaplow occasionally consults on antitrust cases, and his spouse is in the legal department of a financial services firm. Kominers advises firms engaged in marketplace design and development. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research.