Positive Empirical Models of Election Fraud (that May Also Measure Voters’ Strategic Behavior)∗

Positive Empirical Models of Election Fraud (that May Also also Measure Voters’ Strategic Behavior) A landmark in election forensics was the 2012 PNAS paper by Klimek, Yegorov, Hanel and Thurner, which presents the first positive empirical model of election fraud: positive in the sense that the model describes what a fraudulent election looks like and then estimates the amount of fraud (of which there are two types) occurring in a particular election. The model also has the remarkable property of giving pretty much the same estimates regardless of the level of aggregation at which vote counts are observed. Being inspired by complex systems ideas, the Klimek model falls short from a statistical perspective. We modify the Klimek model to improve the shortcomings, introducing chi-squared and finite mixture variants. The resulting models do not appear to be as invariant over levels of aggregation as the original Klimek model. We show that the election fraud probability estimates from the Klimek model (using the chi-squared variant) relate meaningfully to postelection complaints in the 2009 German election and to nullification petitions in the 2006 Mexican election. We also assess how well the fraud parameter estimates predict the complaints and petitions. The complaints and petitions are likely prompted in part by election frauds, so the estimated fraud parameters should relate meaningfully and predictably to them. We also show that the model also is sensitive to the strategies voters are using, at least in Germany. So what the “fraud statistics” measure may be ambiguous. Practical computing difficulties prevent estimating the finite mixture variant for the Germany 2009 and Mexico 2006 data in this version of the paper.