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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