Seeing Double Voting: An Extension of the Birthday Problem

12 Pages Posted: 3 Jul 2007 Last revised: 21 May 2014

See all articles by Michael P. McDonald

Michael P. McDonald

George Mason University - Government and Politics; University of Florida

Justin Levitt

Loyola Law School Los Angeles

Date Written: July 1, 2007


Introductory statistics classes are commonly presented with the Birthday Problem: the surprisingly high probability that two students in the class share the same birthday. Here, we review and extend the Birthday Problem to find the probability that two persons in a given group share an exact birthdate and in a related calculation, the expected number of matching birthdates in a group of a certain size. These thorny calculations are simplified in a simulation framework. We then apply the Birthdate Problem to a pressing legal and public policy debate concerning allegations of widespread double voting and/or multiple registration. We show that these allegations are inflated by not appropriately accounting for the Birthdate Problem, and discuss the implications of the Birthdate Problem for the debate over double voting and the means to address this perceived fraud.

Keywords: birthday problem, matching, fraud, voter fraud, double voting, birthday, name

JEL Classification: C00, C15, C13, K00, K10, K39

Suggested Citation

McDonald, Michael P. and McDonald, Michael P. and Levitt, Justin, Seeing Double Voting: An Extension of the Birthday Problem (July 1, 2007). 7 Election L. J. 111 (2008), 2nd Annual Conference on Empirical Legal Studies Paper, Available at SSRN: or

Michael P. McDonald

George Mason University - Government and Politics ( email )

4400 University Drive
Fairfax, VA 22030
United States

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

Justin Levitt (Contact Author)

Loyola Law School Los Angeles ( email )

919 Albany Street
Los Angeles, CA 90015-1211
United States
213-736-7417 (Phone)
213-380-3769 (Fax)


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