Vote Tampering in a District Justice Election in Beaver County, PA

Abstract

This article examines the evidence of vote tampering in a District Justice election in Beaver County, Pennsylvania. An informal exploratory data analysis and a legal history are followed by a formal Bayesian model of the data from the vote count on election night and the recount completed 2 months later. The evidence suggests that persons unknown could have gained access to the boxes containing the paper ballots, and surprising patterns of changes in the counts support the inference that certain boxes were tampered with. Three methods are compared not only with respect to the overall matter of whether tampering occurred, but also with respect to which precincts were likely to have been tampered with, and to what extent. The results are generally consistent across methods. The Bayesian model is validated by using it on the data for a race (for Superior Court) in the same election in which vote tampering is not suspected. The results show that the model gives a predictive distribution of just a few votes uncertainty for the Superior Court race but of around 60 votes in the District Justice race, enough to swing the election. Technically, the computations involve a Markov chain Monte Carlo. Because it is not possible to observe how each individual ballot was counted each time, data augmentation is required to fill in a Markov matrix given both margins. The fact that both margins are given restricts the kinds of proposals that the chain considers.

KEY WORDS:

• Ballots
• Data augmentation
• Markov chain Monte Carlo