Recent evolutionary models of reproductive partitioning within animal societies (known as 'optimal skew', 'concessions' or 'transactional' models) predict that a dominant individual will often yield some fraction of the group's reproduction to a subordinate as an incentive to stay in the group and help rear the dominant's offspring. These models quantitatively predict how the magnitude of the subordinate's 'staying incentive' will vary with the genetic relatedness between dominant and subordinate, the overall expected group output and the subordinate's expected output if it breeds solitarily. We report that these predictions accord remarkably well with the observed reproductive partitioning between conesting dominant and subordinate queens in the social paper wasp Polistes fuscatus. In particular, the theory correctly predicts that (i) the dominant's share of reproduction, i.e. the skew, increases as the colony cycle progresses and (ii) the skew is positively associated both with the colony's productivity and with the relatedness between dominant and subordinate. Moreover, aggression between foundresses positively correlated with the skew, as predicted by transactional but not alternative tug-of-war models of societal evolution. Thus, our results provide the strongest (quantitative support yet for a unifying model of social evolution.