---
title: "Hypercubewise Preference Aggregation in Multi-Issue Domains"
authors:
  - "Vincent Conitzer"
  - "Jérôme Lang"
  - "Lirong Xia"
doi: "10.5591/978-1-57735-516-8/IJCAI11-038"
url: "https://ijcai.org/proceedings/2011/38"
pdf: "https://ijcai.org/proceedings/2011/0038.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "158-162"
track: ""
keywords:
---

# Hypercubewise Preference Aggregation in Multi-Issue Domains

Vincent Conitzer, Jérôme Lang, Lirong Xia

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 158-162. DOI: [10.5591/978-1-57735-516-8/IJCAI11-038](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-038)

## Abstract

We consider a framework for preference aggregation on multiple binary issues, where agents' preferences are represented by (possibly cyclic) CP-nets. We focus on the majority aggregation of the individual CP-nets, which is the CP-net where the direction of each edge of the hypercube is decided according to the majority rule. First we focus on hypercube Condorcet winners (HCWs); in particular, we show that, assuming a uniform distribution for the CP-nets, the probability that there exists at least one HCW is at least 1-1/e, and the expected number of HCWs is 1. Our experimental results confirm these results. We also show experimental results under the Impartial Culture assumption. We then generalize a few tournament solutions to select winners from (weighted) majoritarian CP-nets, namely Copeland, maximin, and Kemeny. For each of these, we address some social choice theoretic and computational issues.