  We introduce a novel family of mechanisms for constrained allocation problems
which we call local priority mechanisms. These mechanisms are parameterized by
a function which assigns a set of agents, the local compromisers, to every
infeasible allocation. The mechanism then greedily attempts to match agents
with their top choices. Whenever it reaches an infeasible allocation, the local
compromisers move to their next favorite alternative. Local priority mechanisms
exist for any constraint, so this provides a method of constructing new designs
for any constrained allocation problem. We give axioms which characterize local
priority mechanisms. Since constrained allocation includes many canonical
problems as special constraints, we apply this characterization to show that
several well-known mechanisms, including deferred acceptance for school choice,
top trading cycles for house allocation, and serial dictatorship can be
understood as instances of local priority mechanisms. Other mechanisms,
including the Boston mechanism, are not local priority mechanisms. We give
sufficient conditions for a local priority mechanism to be group
strategy-proof. We also provide conditions which enable welfare comparisons
across local priority mechanisms.
