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

Published online by Cambridge University Press:  01 August 2014

David H. Koehler*
Affiliation:
The American University

Abstract

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.

Type
Research Article
Copyright
Copyright © American Political Science Association 1983

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References

Butterworth, L.A research note on the size of winning coalitions. A merican Political Science Review, 1971, 65, 741745.CrossRefGoogle Scholar
Ferejohn, A., Fiorina, M. P., & Weisberg, H. F.Toward a theory of legislative decision. In Ordeshook, P. C. (Ed.), Game theory and political science. New York: New York University Press, 1978.Google Scholar
Hardin, R.Hollow victory: the minimum winning coalition. American Political Science Review, 1976, 70, 12021214.CrossRefGoogle Scholar
Groennings, S., Kelley, E. W., & Leiserson, M. (Eds.). The study of coalition behavior. New York: Holt, Rinehart and Winston, 1970.Google Scholar
Luce, R. D., & Raiffa, H.Games and decisions. New York: Wiley, 1957.Google Scholar
McKelvey, R. D.Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory, 1976, 12, 472482.CrossRefGoogle Scholar
McKelvey, R. D., & Niemi, R.A multi-stage game representation of sophisticated voting for binary procedures. Journal of Economic Theory, 1978, 18, 122.Google Scholar
McKelvey, R. D., Ordeshook, P. C., & Winer, M. D.The competitive solution for n-person games without transferable utility, with an application to committee games. American Political Science Review, 1978, 72, 599615.Google Scholar
Owen, G.Game theory. Philadelphia: W. B. Saunders, 1968.Google Scholar
Plott, C. R.A notion of equilibrium and its possibility under majority rule. American Economic Review, 1967, 57, 787806.Google Scholar
Riker, W. H.Comment on Butterworth. American Political Science Review, 1971, 65, 745747.Google Scholar
Riker, W. H.The theory of political coalitions. New Haven, Conn.: Yale University Press, 1962.Google Scholar
Riker, W. H., & Ordeshook, P. C.An introduction to positive political theory. Englewood Cliffs, N.J.: Prentice-Hall, 1973.Google Scholar
Shepsle, K. A.On the size of winning coalitions. American Political Science Review, 1974, 68, 505518.CrossRefGoogle Scholar
Simpson, P. B.On defining areas of voter choice: Professor Tullock on stable voting. Quarterly Journal of Economics, 1969, 83, 478490.CrossRefGoogle Scholar
Thompson, F.American legislative decision making and the size principle. American Political Science Review, 1979, 73, 11001108.Google Scholar
Von Neumann, J., & Morgenstern, O.The theory of games and economic behavior. Princeton, N.J.: Princeton University Press, 1944.Google Scholar
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