Impossibility of interpersonal social identity diversification under binary preferences

Diverse identities, some socially shared, arise from a person’s affiliation with multiple overlapping communities, which are non-disjoint subsets of persons in society. I prove that identification of each individual with binary preferences or their utility function representation, commonplace in economic theory, implies the impossibility of social-identity diversification of persons. Therefore, if the goal is to explain injustices based on social identity distinctions such as racial discrimination, the conceptual reach of economic theory needs extension. I propose a generalization by assigning non-binary preferences to each individual player to achieve endogenous social diversification, to potentially serve as a basis for explaining discrimination.