# Learning How to Vote with Principles: Axiomatic Insights Into the Collective Decisions of Neural Networks

arXiv: https://arxiv.org/abs/2410.16170 · HTML: https://mlsanity.com/paper/2410.16170/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [A Voting-Based System for Ethical Decision Making](https://mlsanity.com/paper/1709.06692/) (2017)
- [Mapping Social Choice Theory to RLHF](https://mlsanity.com/paper/2404.13038/) (2024)
- [Putting a Compass on the Map of Elections](https://mlsanity.com/paper/2105.07815/) (2021)
- [Learning to Elect](https://mlsanity.com/paper/2108.02768/) (2021)
- [Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers](https://mlsanity.com/paper/2004.02350/) (2020)
- [Properties of the Mallows Model Depending on the Number of Alternatives: A Warning for an Experimentalist](https://mlsanity.com/paper/2401.14562/) (2024)
- [Crowdsourcing for Participatory Democracies: Efficient Elicitation of Social Choice Functions](https://mlsanity.com/paper/1406.7542/) (2014)
- [Learning to Manipulate under Limited Information](https://mlsanity.com/paper/2401.16412/) (2024)

## Built on by (most cited first, 5 of 5)

- [High-Dimensional Data Classification in Concentric Coordinates](https://mlsanity.com/paper/2507.18450/) (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)
- [More Data, Worse Decisions? Preference Reversals in Neural Networks under Gram Incompatibility](https://mlsanity.com/paper/2607.27255/) (2026)

## Abstract (arXiv)

Can neural networks be applied in voting theory, while satisfying the need for transparency in collective decisions? We propose axiomatic deep voting: a framework to build and evaluate neural networks that aggregate preferences, using the well-established axiomatic method of voting theory. Our findings are: (1) Neural networks, despite being highly accurate, often fail to align with the core axioms of voting rules, revealing a disconnect between mimicking outcomes and reasoning. (2) Training with axiom-specific data does not enhance alignment with those axioms. (3) By solely optimizing axiom satisfaction, neural networks can synthesize new voting rules that often surpass and substantially differ from existing ones. This offers insights for both fields: For AI, important concepts like bias and value-alignment are studied in a mathematically rigorous way; for voting theory, new areas of the space of voting rules are explored.