Do redundant bureaucratic arrangements represent wasteful duplication or a hedge against political uncertainty? Previous attempts at addressing this question have treated agency actions as exogenous, thus avoiding strategic issues such as collective action problems or competition. I develop a game-theoretic model of bureaucratic policy making in which a political principal chooses the number of agents to handle a given task. Importantly, agents have policy preferences that may be opposed to the principal's, and furthermore may choose their policy or effort levels. Among the results are that redundancy can help a principal achieve her policy goals when her preferences are not aligned with the agents'. But redundancy is less helpful if even a single agent has preferences relatively close to the principal's. In this environment collective action problems may cause multiple agents to be less effective than a single agent. Redundancy can also be unnecessary to the principal if the agent's jurisdiction can be terminated.