# Learning Resilient Elections with Adversarial GNNs

arXiv: https://arxiv.org/abs/2601.01653 · HTML: https://mlsanity.com/paper/2601.01653/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Learning to Elect](https://mlsanity.com/paper/2108.02768/) (2021)
- [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)
- [A Note on Data Simulations for Voting by Evaluation](https://mlsanity.com/paper/2104.07666/) (2021)

## Abstract (arXiv)

In the face of adverse motives, it is indispensable to achieve a consensus. Elections have been the canonical way by which modern democracy has operated since the 17th century. Nowadays, they regulate markets, provide an engine for modern recommender systems or peer-to-peer networks, and remain the main approach to represent democracy. However, a desirable universal voting rule that satisfies all hypothetical scenarios is still a challenging topic, and the design of these systems is at the forefront of mechanism design research. Automated mechanism design is a promising approach, and recent works have demonstrated that set-invariant architectures are uniquely suited to modelling electoral systems. However, various concerns prevent the direct application to real-world settings, such as robustness to strategic voting. In this paper, we generalise the expressive capability of learned voting rules, and combine improvements in neural network architecture with adversarial training to improve the resilience of voting rules while maximizing social welfare. We evaluate the effectiveness of our methods on both synthetic and real-world datasets. Our method resolves critical limitations of prior work regarding learning voting rules by representing elections using bipartite graphs, and learning such voting rules using graph neural networks. We believe this opens new frontiers for applying machine learning to real-world elections.