You can make a team perfectly diverse in terms of race and gender, but the math says it’s impossible to get it right once you add a third category.
Policy makers often assume that with a large enough candidate pool, perfect intersectional representation is always achievable. This research identifies a 'sharp boundary' where the math fails, proving that once you try to balance three or more traits, you cannot guarantee fair selection for everyone.
Feasible Diversity: Individually Fair Lotteries with Intersectional Constraints
SSRN · 6337900
We study selecting k candidates under intersectional representation constraints, such as race and gender. We identify a sharp boundary. With two diversity dimensions, proportional targets are always jointly feasible. We give an efficient constructive method that outputs an individually fair randomized selection over feasible groups, guaranteeing equal marginal selection probabilities. With three or more dimensions, feasibility can break down. We develop constructive approximation methods that me