This paper tackles the intersection of two trends, the increasing prevalence of flat, so-called horizontal organizations and the greater gender diversity of the workers that such organizations employ. We investigate why these organizations may be more equitable in their allocation practices by turning attention to the allocation of individuals into work groups where the social prominence of the members vary. Analysis of data on 3,575 employees working in R&D over a twenty-five year period indicates that performance affects working with socially-prominent employees, and also that women receive better allocation outcomes from their performance than men. We locate this surprising gender-based advantage for women in their numerical rarity, and surmise that once women are no longer rare in organizations this effect dissipates. In an experiment with 710 participants we find support for our proposition. High performing women receive more favorable allocation outcomes than equally high performing men, but only when women are numerically rare. These two studies inform our understanding of how new ways of organizing intersect with organizational demography and gender diversity, and why, even if there is a tilt toward equality this may decelerate with greater entry of women into horizontal organizations.