# Learning to Elect

arXiv: https://arxiv.org/abs/2108.02768 · HTML: https://mlsanity.com/paper/2108.02768/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 5 Aug 2021.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Deep Graph Library: A Graph-Centric, Highly-Performant Package for Graph Neural Networks](https://mlsanity.com/paper/1909.01315/) (2019)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)

## Built on by (most cited first, 8 of 8)

- [Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks](https://mlsanity.com/paper/2410.16170/) (2024)
- [Learning to Manipulate under Limited Information](https://mlsanity.com/paper/2401.16412/) (2024)
- [Abductive and Contrastive Explanations for Scoring Rules in Voting](https://mlsanity.com/paper/2408.12927/) (2024)
- [What Voting Rules Actually Do: A Data-Driven Analysis of Multi-Winner Voting](https://mlsanity.com/paper/2508.06454/) (2025)
- [EMERGENT: Efficient and Manipulation-resistant Matching using GFlowNets](https://mlsanity.com/paper/2506.12033/) (2025)
- [Learning Resilient Elections with Adversarial GNNs](https://mlsanity.com/paper/2601.01653/) (2026)
- [Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment](https://mlsanity.com/paper/2602.03003/) (2026)
- [AI of the People, by the People, for the People: A Social Choice Approach to Collective Control of Artificial Intelligence](https://mlsanity.com/paper/2605.16291/) (2026)

## Abstract (arXiv)

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.