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arXiv · 1312.6546

Fair assignment of indivisible objects under ordinal preferences

Haris Aziz·Serge Gaspers·Simon Mackenzie·Toby Walsh
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Abstract

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized allocations to systematically define varying notions of proportionality and envy-freeness for discrete assignments. The computational complexity of checking whether a fair assignment exists is studied for these fairness notions. We also characterize the conditions under which a fair assignment is guaranteed to exist. For a number of fairness concepts, polynomial-time algorithms are presented to check whether a fair assignment exists. Our algorithmic results also extend to the case of unequal entitlements of agents. Our NP-hardness result, which holds for several variants of envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang (ECAI 2010). We also propose fairness concepts that always suggest a non-empty set of assignments with meaningful fairness properties. Among these concepts, optimal proportionality and optimal weak proportionality appear to be desirable fairness concepts.

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Haris Aziz, Serge Gaspers, Simon Mackenzie, Toby Walsh. 2013-12-23. Fair assignment of indivisible objects under ordinal preferences. https://arxiv.org/abs/1312.6546

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