Estimating the Probability of Events that Have Never Occured: When is Your Vote Decisive?

Journal of the American Statistical Association, Vol. 93, No. 441, pp. 1-9. March 1998

9 Pages Posted: 16 Jan 2008

See all articles by Andrew Gelman

Andrew Gelman

Columbia University - Department of Statistics and Department of Political Science

Gary King

Harvard University

John Boscardin

University of California, Los Angeles (UCLA)

Abstract

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal "rational choice" models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from state-level forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.

Suggested Citation

Gelman, Andrew and King, Gary and Boscardin, John, Estimating the Probability of Events that Have Never Occured: When is Your Vote Decisive?. Available at SSRN: https://ssrn.com/abstract=1083825

Andrew Gelman (Contact Author)

Columbia University - Department of Statistics and Department of Political Science ( email )

New York, NY 10027
United States
212-854-4883 (Phone)
212-663-2454 (Fax)

Gary King

Harvard University ( email )

1737 Cambridge St.
Institute for Quantitative Social Science
Cambridge, MA 02138
United States
617-500-7570 (Phone)

HOME PAGE: http://gking.harvard.edu

John Boscardin

University of California, Los Angeles (UCLA) ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095
United States

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