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Abstract We study how overlapping identities shape wage gaps, focusing on gender and race in the United States. The extant theoretical and empirical literature typically interprets intersectionality as intersectional discrimination : multiply marginalised groups (e.g., Black women) suffer a distinct wage penalty over and above the additive combination of gender- and race-based wage gaps. We show that this standard empirical operationalisation is fragile because it implicitly embeds a rarely discussed reference-group convention: the cumulative gap is benchmarked against White men, while the “additive” components are often constructed without them,thereby omitting any wage premium uniquely accruing to White men. To address this, we propose a structural decomposition of group mean wages using simple tree diagrams that allocate observed gaps into gender, race, and an interaction component. Crucially, the interaction can be interpreted in two conceptually distinct ways: as an intersectional penalty (multiply marginalised disadvantage) or as excessive privilege (multiply advantaged surplus). We derive closed-form expressions showing that these two interaction terms are mechanically related and that commonly used estimators may therefore misattribute excessive White male privilege to intersectional discrimination. Applying the framework to U.S. wage data and to adjusted gaps from existing studies, we find persistent evidence of excessive White male privilege and little evidence of an additional intersectional penalty in wages. Beyond measurement, we translate the decomposition into political economy and policy design. Treating the estimated excess White male premium as a tax base, we show that redistribution can be structured so that all non–White male groups experience positive net gains, creating scope for broad coalitional support. We compare three stylised redistribution rules, (i) equal per-capita transfers that preserve additive gaps, (ii) proportional scaling that preserves relative gaps, and (iii) a Rawlsian leximin (poorest-first) strategy, highlighting how different normative objectives map into distinct post-redistribution wage structures while maintaining majority support.