Implementing the Borda outcome via truncated scoring rules: a computational study

Abstract

This study is an attempt to empirically understand the likelihood of choosing the Borda outcome through a truncated scoring rule when n voters are asked to report only part of their linear preferences over m alternatives. We run Monte Carlo simulations through a grid search algorithm as we employ an impartial culture model to sample voters' preferences. Given the range of parameter values we consider, we report the truncated scoring rules that maximize the likelihood of implementing the Borda outcome and how the maximum likelihood changes with m and n. We also present our results on the relative performances of some popular truncated voting rules, such as plurality and approval voting, in implementing the Borda outcome and demonstrate that two-level approval voting performs significantly better than the plurality rule. Moreover, we propose the expected Borda rule as a good proxy for the best implementor of the Borda rule among all truncated rules.