And the winner is ... Chevalier de Borda: Neural networks vote according to Borda's Rule

Abstract

We investigate whether neural networks are appropriate tools for selecting between prominent social choice functions. We find that neural networks can learn the unanimity principle and the Pareto property. Building on these two positive results, we train neural networks on the set of profiles possessing Condorcet winners, on the set of profiles possessing a unique Borda winner, and on the set of profiles possessing a unique plurality winner. We investigate which social outcome a neural network chooses if trained on the set of profiles possessing unique winners according to one or more social choice functions. We compare the choices obtained by trained neural networks with those chosen by the Borda count, the Copeland method, the Kem´ eny-Young method, the plurality rule, and 2-approval voting. We find that the trained neural networks’ behavior is the closest to the Borda rule, second closest to the Condorcet-consistent methods, and clearly, the furthest away from the plurality rule. By this approach we hope to give new insight on the problem of selecting the appropriate voting rule.