Ordinal Preference Games: An Analysis of Legislative Coalition Formation Without Transferable Utility

Two important findings from n-person game theory are that coalition formation is superadditive if and only if a game possesses an empty core, and Riker's size principle. Up to the present, both theorems have been proved and critiqued under the assumption of transferable cardinal utility.This analysis eliminates the cardinal utility assumption on the grounds that it is generally inconsistent with the conditions that characterize collective choice on political issues. Instead, a model of collective decision making is set forth in terms of ordinal preferences, and the two theorems are reconsidered. The superadditivity theorem survives intact, whereas the size principle is weakened. Circumstances are identified in which there is no incentive to reduce an oversized winning coalition; however, under no condition is there an incentive to increase the size of a winning coalition. A number of coalition-size hypotheses are tested using roll-call data from the U.S. Senate. The results raise new questions about the role of coalition formation in legislative voting strategy.