Diversity as Majorization

2026-08-11

AI Summary

This study addresses the problem of comparing and selecting optimal groups while jointly accounting for diversity and individual ability. It introduces, for the first time, a systematic framework based on majorization to construct an ordinal diversity preorder that does not presuppose any intrinsic diversity advantage for specific types nor rely on any particular diversity index. Within this framework, the authors integrate reserve-and-quota mechanisms with mechanism design principles to formulate a general criterion capable of identifying groups that are maximal in the sense of diversity. The resulting group selection strategy simultaneously maximizes both diversity and ability, and is shown to be Pareto superior to any alternative approach.

Abstract

How should institutions compare group diversity, and which group should they select when they value diversity and merit? We take a target-based approach that evaluates the entire group composition without treating any type as intrinsically diversity-enhancing. Because different diversity indices may rank groups differently, we instead adapt majorization to construct an ordinal diversity preorder. We show that its maximally diverse selections are exactly those maximizing every index in a broad class. This characterization yields a reserve-and-quota policy that selects a maximally diverse group and, among such groups, the highest-merit agents. Any alternative is less diverse, less meritorious, or both.

Problem

• diversity
• majorization
• group selection
• merit
• ordinal diversity

Innovation

• majorization
• diversity preorder
• group selection
• reserve-and-quota policy
• merit-based allocation