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 {\em 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 .
We propose a notion of fairness for allocation problems in which different agents may have different reservation utilities, stemming from different outside options, or property rights . Fairness is usually understood as the absence of envy, but this can be incompatible with reservation utilities. It is possible that Alice's envy of Bob's assignment cannot be remedied without violating Bob's participation constraint. Instead, we seek to rule out {\em justified envy}, defined as envy for which a remedy would not violate any agent's participation constraint . We show that fairness, meaning the absence of justified envy, can be achieved together with efficiency and individual rationality . We introduce a competitive equilibrium approach with price-dependent incomes obtaining the desired properties .
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endowments
reservation utilities, stemming from different outside options, or property rights
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when agents differ in endowments it is impossible to rule out envy without violating property rights. Instead
this can be incompatible with reservation utilities. It is possible that Alice's envy of Bob's assignment cannot be remedied without violating Bob's participation constraint. Instead,
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the
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property rights
participation constraint
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(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
. We introduce a competitive equilibrium approach with price-dependent incomes obtaining the desired properties