
The Conference Paper Assignment Problem: Using Order Weighted Averages to Assign Indivisible Goods
Motivated by the common academic problem of allocating papers to referee...
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Rotational Diversity in MultiCycle Assignment Problems
In multicycle assignment problems with rotational diversity, a set of t...
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Fair assignment of indivisible objects under ordinal preferences
We consider the discrete assignment problem in which agents express ordi...
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On Reachable Assignments in Cycles and Cliques
The efficient and fair distribution of indivisible resources among agent...
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Legal Assignments and fast EADAM with consent via classical theory of stable matchings
Gale and Shapley's college admission problem and concept of stability (G...
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Welfare Guarantees in Schelling Segregation
Schelling's model is an influential model that reveals how individual pe...
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A MinimumRisk Dynamic Assignment Mechanism Along with an Approximation, Heuristics, and Extension from Single to Batch Assignments
In the classic linear assignment problem, items must be assigned to agen...
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Risk aversion in onesided matching
Inspired by realworld applications such as the assignment of pupils to schools or the allocation of social housing, the onesided matching problem studies how a set of agents can be assigned to a set of objects when the agents have preferences over the objects, but not vice versa. For fairness reasons, most mechanisms use randomness, and therefore result in a probabilistic assignment. We study the problem of decomposing these probabilistic assignments into a weighted sum of expost (Pareto)efficient matchings, while maximizing the worstcase number of assigned agents. This decomposition preserves all the assignments' desirable properties, most notably strategyproofness. For a specific class of probabilistic assignments, including the assignment by the Probabilistic Serial mechanism, we propose a polynomialtime algorithm for this problem that obtains a decomposition in which all matchings assign at least the expected number of assigned agents by the probabilistic assignment, rounded down, thus achieving the theoretically best possible guarantee. For general probabilistic assignments, the problem becomes NPhard. For the Random Serial Dictatorship (RSD) mechanism, we show that the worstcase number of assigned agents by RSD is at least half of the optimal, and that this bound is asymptotically tight. Lastly, we propose a column generation framework for the introduced problem, which we evaluate both on randomly generated data, and on realworld school choice data from the Belgian cities Antwerp and Ghent.
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