The integration of renewable power supplies into existing electrical grids, or other major technology transitions in electric power, is a complex sociotechnical process. While the technical challenges are well-understood, the process of adapting electricity policy and market rules to these new technologies is understudied. Planning and market rules are a critical determinant of the technical success of renewable energy integration efforts and the financial viability of renewable energy investments. Organizational adaptation can be particularly complex in electric power, where transmission grids cross multiple political boundaries and decisions are made not by central authorities or governments, but in cooperative regional frameworks that must accommodate many divergent interests. We add to a recently emerging literature on the governance of regional organizations that plan and operate electric power grids by developing and illustrating a novel approach to the study of political power in multistakeholder electricity organizations. We use semistructured interviews with participants in a specific regional electric grid authority, the PJM Regional Transmission Operator in the Mid-Atlantic United States, to elicit perceptions of where tensions arise in stakeholder-driven processes for changing PJM's rules and perceptions of those groups of stakeholders that possess political power. We treat these perceptions as hypotheses that can be evaluated empirically using five years of data from PJM on how stakeholders voted on a wide variety of regional electricity policy issues. Representing voting behavior as a network, we use a community detection method to identify strong coalitions of stakeholders in PJM that provide support for some stakeholder perceptions of political power and refute other perceptions. The degree distribution of the voting network exhibits a fat tail relative to those in other canonical graph models. We show, using relatively simple network metrics including degree, betweenness, and the mixing parameter, that the reason for this fat tail in the degree distribution is the existence of "swing" voters in RTO stakeholder networks. These voters are identifiable in the tail of the degree distribution of the voting network and are influential in pushing highly contentious rule change proposals towards passage or failure. The method we develop is generalizable to other contexts and provides a new framework for the study of regional electricity policy formation.