This paper compares the incentives to create obstructive committee systems under different constitutionally specified requirements for passing legislation. The Shapley value is used to measure the distribution of bargaining power in the legislature. If the legislature is bicameral or the president can veto, then each chamber of the legislature can increase its total bargaining power, at the expense of the other chamber or the president, by giving its committee chairmen the power to block legislation. This incentive to let committees act as gatekeepers with veto power can persist even when such power may cause some opportunities for beneficial legislation to be lost. This incentive is absent, however, in unicameral parliamentary systems.