Abstract: In voting rights cases, judges often infer unobservable individ ual 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 tradi tional frequentist and Bayesian approaches cannot be employed without first imposing a range of assumptions. In order to mitigate the problems result ing 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.