Affirmative action policies, by establishing representation thresholds for pro-

tected groups, seek to balance fairness and equity in various assignment problems.

Fairness is maintained by prioritizing individuals based on merit scores, while equity

is ensured through guaranteed group representation. We focus on overlapping re-

serves, where individuals can belong to multiple groups, and introduce the Maximal

Score and Minimum Guarantee (MSMG) choice rule, which upholds representation

requirements while preserving fairness. We define the score of an assignment as

the sum of the merit scores of the selected individuals. We demonstrate that the

assignment produced by the MSMG choice rule achieves the highest possible score

among all fair assignments that satisfy the given representation thresholds.

JEL Classification: C78, D47, D63.

Keywords: Matching; Affirmative action; Complementarity; Merit scores.