T his article promotes a characterization of intraparty politics that explains how rank-and-file party members control the delegation of power to their cabinet ministers and shadow cabinet ministers. Using the uncovered set as a solution concept and a measure of party members' collective preferences, we explore the hypothesis that backbenchers' preferences constrain the ministerial selection process in a manner that mitigates agency problems. Specifically, promotion is distributed preferentially to members whose own policy preferences are proximate to the uncovered set of all party members' preferences. Our analysis of ministerial appointments in the contemporary British Parliament supports this view. For both the Labour and Conservative parties, front bench appointments are more sensitive to the collective preferences of backbenchers in each party as measured by the party uncovered set than to the preferences of the parties' leaders.

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The paper offers a reassessment of canonical attempts to address a fundamental question about majority rule: what is the relationship between the preferences held by the participants and the outcomes that emerge from their interactions? Previous work, based on the analysis of abstract spatial models or relying on data from real-world spatial experiments, has yielded a mass of contradictory findings. Our work applies a new technique for estimating the uncovered set, a concept that describes a fundamental constraint on majority rule: given the preferences of decision makers, which outcomes can emerge from majority-rule decision making? By applying the uncovered set to a series of previous experiments on majority rule, we show that their seemingly bizarre and incompatible findings are in fact consistent with a clearly specified theory of how sophisticated individuals make decisions in majority-rule settings.

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We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in ''real-world'' social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.