Structure in Dichotomous Preferences

TL;DR

This paper extends the study of structured preferences in computational social choice to dichotomous preferences, proposing new domain notions and showing that some lead to efficient algorithms for approval-based multi-winner rules.

Contribution

It introduces new notions of single-peaked and single-crossing preferences for dichotomous profiles and demonstrates their usefulness in designing efficient algorithms.

Findings

Certain structured dichotomous domains admit polynomial-time algorithms.

New analogues of classical preference restrictions are proposed for dichotomous preferences.

Some computationally hard approval rules become tractable under these domain restrictions.

Abstract

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter's preference list is a total order of candidates. The goal of this paper is to extend this line of research to the setting where voters' preferences are dichotomous, i.e., each voter approves a subset of candidates and disapproves the remaining candidates. We propose several analogues of the notions of single-peaked and single-crossing preferences for dichotomous profiles and investigate the relationships among them. We then demonstrate that for some of these notions the respective restricted domains admit efficient algorithms for computationally hard approval-based multi-winner rules.