# Pareto Optimal Allocation under Uncertain Preferences

# Pareto Optimal Allocation under Uncertain Preferences

## Haris Aziz, Ronald de Haan, Baharak Rastegari

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

Main track. Pages 77-83.
https://doi.org/10.24963/ijcai.2017/12

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider this 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 these models, we present a number of algorithmic and complexity results highlighting the difference and similarities in the complexity of the two models.

Keywords:

Agent-based and Multi-agent Systems: Social Choice Theory