Government formation is probably the most important consequence of democratic elections. These government formation processes sometimes result in minority governments implying that the political party/parties exercising executive power does/do not hold an absolute majority of legislative seats. Existing literature suggests that minority governments are a result of rational behavior of political parties. As the benefits of governing depend on the parliamentary structure defining power granted to opposition actors, political parties more often refrain from executive office in legislatures that grant more power to opposition parties. To test this argument, the literature has mostly considered the number of standing committees to assess opposition power. This paper argues that focusing exclusively on parliamentary committees neglects important opportunities for opposition players to influence the policy-making process and thereby also the benefits of government participation. The paper goes beyond the usual focus on the number of standing committees and presents a comprehensive data collection effort to assess policy-making power of opposition players. Results show that, although committee strength plays an important role for minority government formation, the rational choice argument about government participation does not necessarily hold when extended beyond the committee system.