Riker's `size principle' predicts that only minimal winning coalitions (MWCs) will form in n-person zero-sum games that satisfy certain conditions. After summarizing the logic of this principle, a model is proposed in which n players can be ordered from most to least weighty. Two different kinds of MWCs are distinguished:
• those in which every member is `critical' (member-MWCs); and
• member-MWCs that have the smallest weight (weight-MWCs).
A member is critical when its defection causes an MWC to become losing. A listing of the possible categories of member-MWCs indicates that their numbers rapidly increase with the number of players (2, 6, 20, and 116 for n = 3, 4, 5, and 6 players). Three quantitative measures of bargaining power show that less weighty players may, on occasion, be more powerful than more weighty players. Possible empirical manifestations of the inverse relationship between weight and bargaining power in parliamentary coalitions and international politics are discussed.
Banzhaf, John F., III
(1965) `Weighted Voting Doesn't Work: A Mathematical Analysis', Rutgers Law Review19(2): 317-343.
2.
Brams, Steven J.
(1968) `Measuring the Concentration of Power in Political Systems', American Political Science Review63(2): 461-475.
3.
Brams, Steven J.
(1969) `The Structure of Influence Relationships in the International System', in James N. Rosenau (ed.), International Politics and Foreign Policy: A Reader in Research and Theory,2nd edn, pp. 583-599. New York: Free Press.
4.
Brams, Steven J.
(1975) Game Theory and Politics. New York: Free Press.
5.
Brams, Steven J.
(1985) Rational Politics: Decisions, Games, and Strategy. Washington DC: CQ Press (reprinted by Academic Press, 1989).
6.
Brams, Steven J.
(1990) Negotiation Games: Applying Game Theory to Bargaining and Arbitration. New York: Routledge.
7.
Brams, Steven J.
, Dan S. Felsenthal and Zeev Maoz (1986) `New Chairman Paradoxes', in Andreas Diekmann and Peter Mitter (eds) Paradoxical Effects of Social Behavior: Essays in Honor of Anatol Rapoport, pp. 243-256. Heidelberg: Physica-Verlag.
8.
Brams, Steven J.
, Dan S. Felsenthal and Zeev Maoz (1988) `Chairman Paradoxes under Approval Voting', in Gerald Eberlein and Hal Berghel (eds), Theory and Decision: Essays in Honor of Werner Leinfellner pp. 223-233. Dordrecht: D. Reidel.
9.
Budge, Ian
and Hans Keman (1990) Parties and Democracy: Coalition Formation and Government Functioning in Twenty States. Oxford: Oxford University Press.
10.
Caplow, Theodore
(1956) `A Theory of Coalitions in the Triad', American Sociological Review21(4): 489-493.
11.
Caplow, Theodore
(1959) `Further Developments of a Theory of Coalitions in the Triad', American Journal of Sociology64 (March): 488-493.
12.
Caplow, Theodore
(1968) Two Against One: Coalitions in Triads. Englewood Cliffs NJ: Prentice-Hall.
13.
Deegan, John, Jr.
and Edward E. Packel (1983) `To the (Minimal Winning) Victors Go the (Equally Divided) Spoils: A New Power Index for Simple n-Person Games', in Steven J. Brams, William F. Lucas and Philip D. Straffin, Jr (eds), Modules in Applied Mathematics: Political and Related Models, vol. 2, pp. 239-255. New York: Springer-Verlag.
14.
Farquharson, Robin
(1969) Theory of Voting. New Haven, CT: Yale University Press.
15.
Fishburn, Peter C. and Steven J. Brams (1994) `Minimal Winning Coalitions in Weighted-Majority Voting Games', preprint, Dpt of Politics, New York University.
16.
Fox, Annette Baker
(1959) The Power of Small States: Diplomacy in World War II. Chicago: University of Chicago Press.
17.
Gamson, William A.
(1961) `A Theory of Coalition Formation', American Sociological Review26(3): 373-382.
18.
Habeeb, William Mark
(1988) Power and Tactics in International Negotiation: How Weak Nations Bargain with Strong Nations. Baltimore, MD: Johns Hopkins University Press.
19.
Holler, Manfred J.
(ed.) (1982) Power, Voting, and Voting Power. Würzburg: Physica-Verlag.
20.
Lambert, J. P.
(1988) `Voting Games, Power Indices, and Presidential Elections', UMAP Journal9(3): 213-267.
21.
Laver, M. J.
and Ian Budge (eds) (1992) Party Policy and Government Coalitions. New York: St Martin's Press.
22.
Laver, Michael
and Norman Schofield (1990) Multiparty Government: The Politics of Coalition in Europe. Oxford: Oxford University Press.
23.
Lucas, William F.
(1992) Fair Voting: Weighted Votes for Unequal Constituencies, Histomap Module 19. Lexington, KY: COMAP.
24.
Luce, R. Duncan
and Arnold A. Rogow (1956) `A Game-Theoretic Analysis of Congressional Power Distributions for a Stable Two-Party System', Behavioral Science1 (April): 83-95.
25.
Maoz, Zeev
(1990) Paradoxes of War: On the Art of National Self-Entrapment. Boston, MA: Unwin Hyman.
26.
Paul, T.V.
(1994) Asymmetric Conflicts: War Initiation by Weaker Powers. Cambridge: Cambridge University Press.
27.
Riker, William H.
(1962) The Theory of Political Coalitions. New Haven, CT: Yale University Press.
28.
Riker, William H.
and Peter C. Ordeshook (1973) An Introduction to Positive Political Theory. Englewood Cliffs, NJ: Prentice-Hall.
29.
Shapley, L. S.
and Martin Shubik (1954) `A Method of Evaluating the Distribution of Power in a Committee System', American Political Science Review48(3): 787-792.
30.
Straffin, Philip D.
(1993) Game Theory and Strategy. Washington DC: Mathematical Association of America.
31.
Vital, David
(1971) The Survival of Small States: Studies in Small Power/Great Power Conflict. Oxford: Oxford University Press.
32.
Willis, Richard H.
(1962) `Coalitions in the Tetrad', Sociometry25(4): 358-376.
33.
Zagare, Frank C.
(1979) `The Geneva Conference Game of 1954: A Case of Tacit Deception', International Studies Quarterly23(3): 390-411.
