# Preference Restrictions in Computational Social Choice: A Survey

arXiv: https://arxiv.org/abs/2205.09092 · HTML: https://mlsanity.com/paper/2205.09092/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2022.

## Built on by (most cited first, 9 of 9)

- [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)
- [Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences](https://mlsanity.com/paper/2604.05953/) (2026)
- [Beyond Arrow: From Impossibility to Possibilities in Multi-Criteria Benchmarking](https://mlsanity.com/paper/2602.07593/) (2026)
- [Snowveil: A Framework for Decentralised Preference Discovery](https://mlsanity.com/paper/2512.18444/) (2025)
- [Open Problems in Differentiable Social Choice: Learning Mechanisms, Decisions, and Alignment](https://mlsanity.com/paper/2602.03003/) (2026)
- [Algorithms for Structured Elections under Thiele Voting Rules](https://mlsanity.com/paper/2607.28575/) (2026)
- [Outer Diversity of Condorcet Domains](https://mlsanity.com/paper/2610.00720/) (2026)

## Abstract (arXiv)

Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted.