# Outer Diversity of Condorcet Domains

arXiv: https://arxiv.org/abs/2610.00720 · HTML: https://mlsanity.com/paper/2610.00720/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [Preference Restrictions in Computational Social Choice: A Survey](https://mlsanity.com/paper/2205.09092/) (2022)
- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [Diversity of Structured Domains via k-Kemeny Scores](https://mlsanity.com/paper/2509.15812/) (2025)
- [Outer Diversity of Structured Domains](https://mlsanity.com/paper/2602.15708/) (2026)
- [Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results](https://mlsanity.com/paper/2007.06549/) (2020)

## Abstract (arXiv)

A Condorcet domain is a set of rankings over a given candidate set, such that every election that consists only of (an odd number of) votes from the domain has a transitive majority relation. We study outer diversity of Condorcet domains, i.e., a measure that quantifies expected swap distance from a random vote to a closest one in the domain. We numerically analyze outer diversity for maximal Condorcet domains with few candidates, and then we establish its asymptotic behavior for several special domains, mostly obtaining theoretical results.