This 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.