Computing and Testing Pareto Optimal Committees

TL;DR

This paper investigates the computational complexity of identifying Pareto optimal committees under various preference extensions, providing efficient algorithms and analyzing strategic behavior in committee selection.

Contribution

It introduces a comprehensive study of Pareto optimality for committee selection with multiple preference extensions, including efficient algorithms and strategic considerations.

Findings

Linear-time algorithms for Pareto optimal and strategyproof committee selection

Complexity results for computing and verifying Pareto optimal outcomes

Analysis of strategic issues in committee selection processes

Abstract

Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider five prominent extensions (responsive, downward lexicographic, upward lexicographic, best, and worst). For each of them, we consider the corresponding Pareto optimality notion, and we study the complexity of computing and verifying Pareto optimal outcomes. We also consider strategic issues: for four of the set extensions, we present a linear-time, Pareto optimal and strategyproof algorithm that even works for weak preferences.