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While legislatures typically use majority rule to allocate a budget in distributive legislation, near-unanimous consent over the broad allocation of benefits is pervasive. I develop a game-theoretic model where players strategically interact in a universal coalition to determine allocations, with non-cooperative bargaining as a threat point for the breakdown of cooperation. To quantify the effects of political power and actual needs on the agreed-upon allocation, I structurally estimate the model using the "Bridge Bill Capital Budget" in 1992. I find that 9.58% of the budget would be allocated differently if allocations were determined only based on actual needs.