Alliance formation is a multilateral process. The vast majority of alliance relations are created via multilateral alliances. Moreover, leaders assess the alliance as a whole, not just each prospective partner. Any alliance could have three or more members, so one must understand not just why third parties were included in multilateral alliances, but why they were excluded from bilateral alliances. Unfortunately, current research treats alliance formation as a bilateral process: it theorizes about bilateral alliances and tests hypotheses using dyadic research designs. Reconceptualizing all alliances as originating from a multilateral process reveals that a long-neglected theory, William Riker’s size principle, illuminates the role of power in alliance formation. Using k-adic data to analyze multilateral processes, we find strong support for Riker’s claim about minimum winning coalitions in world politics. Our argument and findings, by highlighting how a fundamental state behavior like alliance formation follows a multilateral process, suggest rethinking much of international relations research.