Statistical Properties of Social Choice Mechanisms

Most previous research on statistical approaches to social choice focused on the computation and characterization of maximum likelihood estimators (MLE) of various parametric ranking models. In this paper, we take a traditional statistical approach by evaluating social choice mechanisms w.r.t. two important statistical criteria: (1) consistency, a minimum requirement for reasonable estimators, and (2) minimaxity, a well-accepted optimality criterion. For consistency, we propose a new and general class of social choice mechanisms called generalized outcome scoring rules (GOSR) that include many commonly studied social choice mechanisms. Given any ranking model, we fully characterize all GOSRs that are consistent estimators of it, and derive an upper bound on the convergence rate. We also showed that the bound is asymptotically tight for some GOSR and ranking model. This allows us to fully characterize all GOSRs that are consistent w.r.t. some model. For minimaxity, we characterize a class of minimax estimators for neutral ranking models. As a corollary, the uniformly randomized MLE has the highest probability to correctly reveal the ground truth among all estimators for a number of natural ranking models.