  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.
