Computing and Testing Pareto Optimal Committees
This work addresses committee selection issues in social choice theory, providing computational insights and algorithms for practical applications, though it is incremental as it builds on existing preference extensions.
The paper tackles the problem of selecting committees based on agent preferences, focusing on Pareto optimality as a minimal requirement, and analyzes the computational complexity of computing and verifying Pareto optimal outcomes for five preference extensions, while also presenting a linear-time, Pareto optimal, and strategyproof algorithm for four of these extensions.
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.