Title:      Statistics for Digits

Authors:    Walter Mebane

Entrydate:  2007-07-17 13:08:24

Keywords:   election forensics, 2BL test, Benford's Law, vote
counts, outliers, anomalies, election fraud

Abstract:   I show how election results may be used to calibrate
a test that compares the second digits of a set of precinct-level
vote counts to the frequencies expected according to Benford's
law.  For the votes cast for two competing candidates, the
calibration is accomplished by tuning a simulation mechanism
that mixes normal and negative binomial distributions so that
the first two moments of the simulated distribution match the
moments observed in a set of precincts.  I illustrate the method
using data from the counties that had the ten largest values of
the digit test statistic for the major party candidates in the
2000 and 2004 U.S. presidential election.  Calibration suggests
that the peculiar features of the joint distribution of
candidate support and precinct sizes explain several of the
large test statistic values.  I show that artificial
manipulations can significantly increase the test statistic's
value even relative to the increased distribution the tuned
mechanism is producing.  So the test can sometimes detect
systematic distortions in vote counts even when the baseline
mechanism does not produce counts that have digits that are
distributed as specified by Benford's law.

http://polmeth.wustl.edu/retrieve.php?id=708