Election Forensics: Vote Counts and Benford’s Law
∗
Walter R. Mebane, Jr.†
July 17, 2006
∗Prepared for presentation at the 2006 Summer Meeting of the Political Methodology Society,
UC-Davis, July 20–22. Previous versions of parts of this paper were presented at the 2006 Annual
Meeting of the Midwest Political Science Association and at seminars at Washington University and
the University of Michigan. Thanks to Daniel Dauplaise for sparking my interest in Benford’s Law,
and to Charlie Gibbons for assistance. I thank David Dill, Martha Mahoney and Luis Gutiérrez
for supplying data and explaining various issues. Thanks to Jasjeet Sekhon and Jonathan Wand
for helpful comments.
†Professor, Department of Government, Cornell University, 217 White Hall, Ithaca, NY 14853–7901
(Phone: 607-255-2868; Fax: 607-255-4530; E-mail: wrm1@cornell.edu).
Abstract
Election Forensics: Vote Counts and Benford’s Law
How can we be sure that the declared election winner actually got the most votes? Was the
election stolen? This paper considers a statistical method based on the pattern of digits in vote
counts (the second-digit Benford’s Law, or 2BL) that may be useful for detecting fraud or other
anomalies. The method seems to be useful for vote counts at the precinct level but not for counts
at the level of individual voting machines, at least not when the way voters are assigned to
machines induces a pattern I call “roughly equal division with leftovers” (REDWL). I
demonstrate two mechanisms that can cause precinct vote counts in general to satisfy 2BL. I use
simulations to illustrate that the 2BL test can be very sensitive when vote counts are subjected to
various kinds of manipulation. I use data from the 2004 election in Florida and the 2006 election
in Mexico to illustrate use of the 2BL tests.
Fraudulent elections and disputes about election outcomes are nothing new. Gumbel (2005)
reviews the sorry history of deceit and electoral manipulation in America, going back to the dawn
of the republic. Throughout the world, in old and new d