Fair bipartite flows

We discuss bilateral assignment under capacity constraints, under the relevant version of the celebrated Consistency axiom: an assignment matrix is globally fair if and only if it is locally fair. When the unconstrained proportional assignment is the ideal assignment, the only consistent approximation under our constraints minimizes the entropy of the assignment matrix; exactly like the Mutual Information index of segregation.  More general consistent assignment rules minimize a common additive welfare function over the entries of the matrix. Examples include maximizing the Nash product of the entries, and, in a limit sense, maximizing the leximin ordering of these entries.

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