Learning to Elect

Abstract

Voting systems have a wide range of applications including recommender systems, web search, product design and elections. Limited by the lack of general-purpose analytical tools, it is difficult to hand-engineer desirable voting rules for each use case. For this reason, it is appealing to automatically discover voting rules geared towards each scenario. In this paper, we show that set-input neural network architectures such as Set Transformers, fully-connected graph networks and DeepSets are both theoretically and empirically well-suited for learning voting rules. In particular, we show that these network models can not only mimic a number of existing voting rules to compelling accuracy -both position-based (such as Plurality and Borda) and comparison-based (such as Kemeny, Copeland and Maximin)but also discover near-optimal voting rules that maximize different social welfare functions. Furthermore, the learned voting rules generalize well to different voter utility distributions and election sizes unseen during training. IntroductionVoting systems are highly prevalent in our daily lives. Examples range from large scale democratic elections to company or family-wide decision making, recommender systems and product design [Boutilier et al., 2015].As with any social decision-making process, the goal of designing voting rules is to reconcile differences and maximize some collective objective. The area of research that studies different voting rules and the approaches to designing them is called voting theory.A vast number of voting rules have been proposed over the years. Among them is the widely applied plurality rule. Despite being simple and intuitive, the plurality rule is very limited in that it does not consider the strength of voters' preferences. Other examples of voting rules, such as Borda and Copeland, take into consideration the ranked preferences of the voters.Voting theorists have developed different approaches to designing voting rules. For example, the axiomatic approach constrains the voting rules to satisfy certain desired properties (axioms) such as anonymity (treating all voters equally) and neutrality (treating all candidates equally). The utilitarian approach, on the other hand, aims to maximize a pre-defined notion of social welfare -a scalar quantity that measures the quality of the elected candidate in the eyes of the electorate.There are major hurdles to overcome in the traditional way of designing and implementing voting rules. First, the celebrated Arrow's Theorem states the nonexistence of non-dictatorship voting rules that simultaneously satisfy a set of seemingly sensible axioms [Arrow et al., 1951]. Second, for some voting rules such as the ones based on pairwise comparisons, finding the winner can be computationally expensive, making them infeasible for large-scale applications. Last but not least, for the utilitarian approach, it is not obvious how to design voting rules that maximize a given notion * Equal contribution.Preprint. Under review.