Conflict management is one of the primary requirements for social complexity. Of the many forms of conflict management, one of the rarest and most interesting is third-party policing, or intervening impartially to control conflict. Third-party policing should be hard to evolve because policers personally pay a cost for intervening, while the benefits are diffused over the whole group. In this study we investigate the incidence and costs of policing in a primate society. We report quantitative evidence of non-kin policing in the nonhuman primate, the pigtailed macaque. We find that policing is effective at reducing the intensity of or terminating conflict when performed by the most powerful individuals. We define a measure, social power consensus, that predicts effective low-cost interventions by powerful individuals and ineffective, relatively costly interventions by low-power individuals. Finally, we develop a simple probabilistic model to explore whether the degree to which policing can effectively reduce the societal cost of conflict is dependent on variance in the distribution of power. Our data and simple model suggest that third-party policing effectiveness and cost are dependent on power structure and might emerge only in societies with high variance in power.