Abstract
The assignment problem is one of the most wellstudied 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 pro-
files. 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