Fairness and efficiency for probabilistic allocations with endowments
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We propose a notion of fairness for allocation problems in which different agents may have different endowments. Fairness is usually understood as the absence of envy, but when agents differ in endowments it is impossible to rule out envy without violating property rights. Instead we seek to rule out justified envy, defined as envy for which the remedy would not violate any agent's property rights. We show that fairness, meaning the absence of justified envy, can be achieved together with efficiency and individual rationality (respect for property rights). Our approach requires standard assumptions on agents' preferences, and is compatible with quantity constraints on allocations. The main application of our results is to school choice, where we can simultaneously achieve fairness, efficiency, and diversity-motivated quantity constraints.
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