Voting: A machine learning approach

Voting rules can be assessed from quite different perspectives: the axiomatic, the pragmatic, in terms of computational or conceptual simplicity, susceptibility to manipulation, and many others aspects. In this paper, we take the machine learning perspective and ask how prominent voting rules compare in terms of their learnability by a neural network. To address this question, we train the neural network to choosing Condorcet, Borda, and plurality winners, respectively. Remarkably, our statistical results show that, when trained on a limited (but still reasonably large) sample, the neural network mimics most closely the Borda rule, no matter on which rule it was previously trained. The main overall conclusion is that the necessary training sample size for a neural network varies significantly with the voting rule, and we rank a number of popular voting rules in terms of the sample size required.