Recovering Vote Choice from Partial Incomplete Data

In voting rights cases, judges often infer unobservable individual vote choices from election data aggregated at the precinct level. That is, one must solve an ill-posed inverse problem to obtain the critical information used in these cases. The ill-posed nature of the problem means that traditional frequentist and Bayesian approaches cannot be employed without first imposing a range of assumptions. In order to mitigate the problems resulting from incorporating potentially inaccurate information in these cases, we propose the use of information theoretic methods as a basis for recovering an estimate of the unobservable individual vote choices. We illustrate the empirical non-parametric likelihood methods with some election data.