Seeing Double Voting: An Extension of the Birthday Problem

Abstract

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