# Most Equitable Voting Rules

arXiv: https://arxiv.org/abs/2205.14838 · HTML: https://mlsanity.com/paper/2205.14838/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 33 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 4 of 4)

- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [The Smoothed Possibility of Social Choice](https://mlsanity.com/paper/2006.06875/) (2020)
- [Semi-Random Impossibilities of Condorcet Criterion](https://mlsanity.com/paper/2107.06435/) (2021)

## Abstract (arXiv)

In social choice theory, anonymity (all agents being treated equally) and neutrality (all alternatives being treated equally) are widely regarded as ``minimal demands'' and ``uncontroversial'' axioms of equity and fairness. However, the ANR impossibility -- there is no voting rule that satisfies anonymity, neutrality, and resolvability (always choosing one winner) -- holds even in the simple setting of two alternatives and two agents. How to design voting rules that optimally satisfy anonymity, neutrality, and resolvability remains an open question. We address the optimal design question for a wide range of preferences and decisions that include ranked lists and committees. Our conceptual contribution is a novel and strong notion of most equitable refinements that optimally preserves anonymity and neutrality for any irresolute rule that satisfies the two axioms. Our technical contributions are twofold. First, we characterize the conditions for the ANR impossibility to hold under general settings, especially when the number of agents is large. Second, we propose the most-favorable-permutation (MFP) tie-breaking to compute a most equitable refinement and design a polynomial-time algorithm to compute MFP when agents' preferences are full rankings.