Pareto Optimal Allocation under Uncertain Preferences

TL;DR

This paper investigates the computational challenges of finding and analyzing Pareto optimal allocations when agents' preferences are uncertain, under two probabilistic models, providing new algorithms and complexity insights.

Contribution

It introduces novel algorithms and complexity results for computing Pareto optimal allocations under uncertainty in preferences, addressing two natural probabilistic models.

Findings

Algorithms for computing the probability of Pareto optimality

Complexity results for the decision problems under uncertainty

Existence results for Pareto optimal assignments with probability one

Abstract

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under two natural uncertainty models: (1) the lottery model in which each agent has an independent probability distribution over linear orders and (2) the joint probability model that involves a joint probability distribution over preference profiles. For both of the models, we present a number of algorithmic and complexity results.