Vote tampering in a district justice election in Beaver County, PA

This article examines the evidence of vote tampering in a District Justice election in Beaver County, Pennsylvania. An informal exploratory data analy sis 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 l ater. The evidence suggests that persons unknown could have gained access t o the boxes containing the paper ballots. and surprising patterns of change s 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, bur also with respect to which precincts were likely to have been tampered with, and to what extent. The results are gene rally consistent across methods. The Bayesian model is validated by using i t 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 p redictive distribution of just a few votes uncertainty for the Superior Cou rt race but of around 60 votes in the District Justice race, enough to swin g 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 matri x given both margins. The bet that both margins are given restricts the kin ds of proposals that the chain considers.