  We consider the problem of dividing items between individuals in a way that
is fair both in the sense of distributional fairness and in the sense of not
having disparate impact across protected classes. An important existing
mechanism for distributionally fair division is competitive equilibrium from
equal incomes (CEEI). Unfortunately, CEEI will not, in general, respect
disparate impact constraints. We consider two types of disparate impact
measures: requiring that allocations be similar across protected classes and
requiring that average utility levels be similar across protected classes. We
modify the standard CEEI algorithm in two ways: equitable equilibrium from
equal incomes, which removes disparate impact in allocations, and competitive
equilibrium from equitable incomes which removes disparate impact in attained
utility levels. We show analytically that removing disparate impact in outcomes
breaks several of CEEI's desirable properties such as envy, regret, Pareto
optimality, and incentive compatibility. By contrast, we can remove disparate
impact in attained utility levels without affecting these properties. Finally,
we experimentally evaluate the tradeoffs between efficiency, equity, and
disparate impact in a recommender-system based market.
