---
title: "Multi-Dimensional Single-Peaked Consistency and Its Approximations"
authors:
  - "Xin Sui"
  - "Alex Francois-Nienaber"
  - "Craig Boutilier"
doi: ""
url: "https://ijcai.org/proceedings/2013/63"
pdf: "https://ijcai.org/proceedings/2013/0063.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "375-381"
track: ""
keywords:
---

# Multi-Dimensional Single-Peaked Consistency and Its Approximations

Xin Sui, Alex Francois-Nienaber, Craig Boutilier

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 375-381.

## Abstract

Single-peakedness is one of the most commonly used domain restrictions in social choice. However, the extent to which agent preferences are single-peaked in practice, and the extent to which recent proposals for approximate single-peakedness can further help explain voter preferences, is unclear. In this article, we assess the ability of both single-dimensional and multi-dimensional approximations to explain preference profiles drawn from several real-world elections. We develop a simple branch-and-bound algorithm that finds multi-dimensional, single-peaked axes that best fit a given profile, and which works with several forms of approximation. Empirical results on two election data sets show that preferences in these elections are far from single-peaked in any one-dimensional space, but are nearly single-peaked in two dimensions. Our algorithms are reasonably efficient in practice, and also show excellent anytime performance.