A pessimist’s approach to one-sided matching

Inspired by real-world applications such as the assignment of pupils to schools or allocation social housing, one-sided matching problem studies how a set agents can be assigned objects when have preferences over objects, but not vice versa. For fairness reasons, most mechanisms use randomness, and therefore result in probabilistic assignment. We study decomposing these assignments into weighted sum ex-post (Pareto-)efficient matchings, while maximizing worst-case number agents. This decomposition preserves all assignments' desirable properties, notably strategy-proofness. specific class assignments, including Probabilistic Serial mechanism, we propose polynomial-time algorithm for this that obtains which matchings assign at least expected assignment, rounded down, thus achieving theoretically best possible guarantee. general becomes NP-hard. Random Dictatorship show is half optimal, bound asymptotically tight. Lastly, column generation framework introduced problem, evaluate both on randomly generated data, school choice data from Belgian cities Antwerp Ghent.