Proportional allocation of indivisible resources under ordinal and uncertain preferences.

We study a fair resource allocation problem with indivisible items. The agents’ preferences over items are assumed to be ordinal and have uncertainties. We adopt stochastic dominance proportionality as our fairness notion and study a sequence of problems related to finding allocations that are fair with a high probability. We provide complexity analysis for each problem and efficient algorithms for some problems. Finally, we propose several heuristic algorithms to find an allocation that is fair with the highest probability. We thoroughly evaluate the performance of the algorithms on both synthetic and real datasets.