The three prevailing accounts of how intergovernmental organizations (IGOs) affect world politics oversimplify significantly, providing incomplete accounts of how IGOs gain influence with member governments. The power-centered and delegation accounts focus primarily on the activities of the governments of major states, leading to significant under-estimation of how the IGO’s head and staff and the governments of other member states also matter in shaping an IGO’s impact. The autonomous bureaucracy account focuses mainly on the activities of the IGO’s head and staff, leading to over-estimation of the IGO’s ability to influence the member states. Descriptively, analyzing an IGO and the member state governments as co-participants in an authority relationship draws attention to the importance of shared procedural and substantive expectations; analytically it promotes a better understanding of how IGOs affect world politics by including all of the co-participants. This avoids the mis-estimations encouraged by prevailing accounts and, by foregrounding continuities and changes in shared expectations, provides a better starting point for comprehending changes in an IGO’s own activities and its relations with member states over time.