This paper presents a finite-horizon, game-theoretic model of the dynamics of multidimensional collective choice and a set of analytical and computational results characterizing those dynamics. The focus is on continuing collective goods programs that have the property that the current policy remains in effect until new legislation is passed. Continuing policies are at the center of government activity and include entitlements, regulations, antitrust law, tax policy, and international trade policy. Changes in some of these program occur frequently,and the theory and computational results provide insights into those changes in the context of a simple game. Despite its simplicity, the game is remarkably poorly-behaved due to the opportunity of agenda setters to choose among majorities, resulting in discontinuities in the value functions of the game.