¹ The basic source here is Arrow, Kenneth J., Social Choice and Individual Values, 2d ed. (New York: John Wiley, 1963Google Scholar). Two other useful sources are Sen, Amartya K., Collective Choice and Social Welfare (San Francisco:Holden-Day, 1970Google Scholar), and Plott, Charles R., “Axio-matic Social Choice Theory: An Overview and Interpretation,” American Journal of Political Science 20 (August 1976), 511CrossRefGoogle Scholar–96.

² Only ordinal preferences are considered in Arrow's theorem. That is, the actors each have a preference ordering that ranks the outcomes from first to worst without specifying the magnitude of the differences between outcomes. Cardinal preferences capture an actor's willingness to take risks in a utility function where expected utility translates to preference over lotteries. Thus, there are many possible sets of cardinal preferences for a given set of ordinal preferences.

³ Sen(fn. i), 173–86.

⁴ The point that preference and structure in conjunction produce social outcomes is developed by Riker, William H. in “Implications from the Disequilibrium of Majority Rule for the Study of Institutions,” American Political Science Review 74 (June 1980), 432CrossRefGoogle Scholar–46.

⁵ The initial effort at the formal analysis of structure in legislatures is by Shepsle, Kenneth A., “Institutional Arrangements and Equilibrium in Multidimensional Voting Models,” American Journal of Political Science 23 (February 1979), 27–59CrossRefGoogle Scholar. Formal analyses of how com mittees can use their position within the legislative process to obstruct legislation are given in Denzau, Arthur T. and Mackey, Robert J., “Gatekeeping and Monopoly Power of Committees: An Analysis of Sincere and Sophisticated Behavior,” American Journal of Political Science 27 (November 1983), 740CrossRefGoogle Scholar–61, and Krehbiel, Keith, “Obstruction and Representative-ness in Legislatures,” American Journal of Political Science 29 (August 1985), 643CrossRefGoogle Scholar–59.

⁶ On the topic of structural change in legislatures, a formal perspective is provided by Shepsle, Kenneth A., “Institutional Equilibrium and Equilibrium Institutions,” in Weisberg, Herbert F., ed., Political Science: The Science of Politics (New York:Agathon Press, 1986), 51–81Google Scholar.

⁷ See Robinson, William A., Thomas B. Reed: Parliamentarian (New York:Dodd, Mead, & Company, 1930). I am indebted to Keith Krehbiel for this example.Google Scholar

⁸ Riker (fn. 4), 445.

⁹ Waltz, Kenneth N., in Theory of International Politics (New York:Random House, 1979Google Scholar), argues that alliances can never be considered structural, but this opinion arises from his balance-of-power view, in which all alliances must be temporary.

¹⁰ This well-known definition is from Krasner, Stephen D., “Structural Causes and Regime Consequences: Regimes as Intervening Variables,” in Krasner, , ed., International Regimes (Ithaca, NY:Cornell University Press, 1983), 1–21Google Scholar, at 1.

¹¹ The following discussion draws heavily on Keohane, Robert O., After Hegemony: Cooperation and Discord in the World Political Economy (Princeton:Princeton University Press, 1984), 85–109Google Scholar.

¹² Mansbach, Richard W. and Vasquez, John A., In Search of Theory: A New Paradigm Global Politics (New York:Columbia University Press, 1981Google Scholar), contend that international politics is a struggle over the resolution of issues. My definition of issues corresponds to their definition of stakes: “objects that are seen as possessing or representing values” (p. 58). Elsewhere, I have presented an elaborate formal model of crisis in which the parties contest the resolution of international issues; see James D. Morrow, “A Spatial Model of International Conflict,” American Political Science Review 80 (December 1986), 1131–50.

¹³ Young, Oran R., “Anarchy and Social Choice: Reflections on the International Polity,” World Politics 30 (January 1978), 241CrossRefGoogle Scholar–63, at 250.

¹⁴ This conclusion follows from the correspondence between the Nash solution and the Zeuthen model of bargaining. In the latter, greater willingness to take risks will force the other side to make additional concessions at some point in the negotiations. The original source for the Nash bargaining solution is Nash, John F., “The Bargaining Problem,” Econ-ometrica 18 (April 1950), 155CrossRefGoogle Scholar–62. John C. Harsanyi has shown that the Nash bargaining solution arises from negotiations where the party with more to lose makes an additional concession in each round of bargaining; see Harsanyi, , “Approaches to the Bargaining Problem Before and After the Theory of Games,” Econometrica 24 (April 1956), 144CrossRefGoogle Scholar–56.

¹⁵ See, for example, the distinction between soft and hard sellers and their consequences for the solution, in Fudenberg, Drew and Tirole, Jean, “Sequential Bargaining with Incomplete Information,” Review of Economic Studies 50 (April 1983), 221CrossRefGoogle Scholar–47. A fine source for further reading on recent developments in bargaining theory is Roth, Alvin E., ed., Game-Theoretic Models of Bargaining (New York:Cambridge University Press, 1985CrossRefGoogle Scholar).

¹⁶ Once again, this point follows from the Nash bargaining solution (fn. 14). Evidence to this effect is provided by Rosen, Stephen in “War Power and the Willingness to Suffer,” in Russett, Bruce, ed., War, Peace, and Numbers (Beverly Hills, CA:Sage, 1972Google Scholar), and Maoz, Zeev, “Resolve, Capabilities, and the Outcomes of Interstate Disputes, 1815–1976,” Journal of Conflict Resolution 27 (June 1983), 195–229CrossRefGoogle Scholar.

¹⁷ This point is examined formally in Morrow, James D., “A Continuous-Outcome Expected Utility Theory ofWaro,” Journal ofConflict Resolution 29 (September 1985), 473–502CrossRefGoogle Scholar.

¹⁸ For an elaboration of this argument, see Mueller, John E., “The Search for the ‘Breaking Point’ in Vietnam,” International Studies Quarterly 24 (September 1980), 497–519CrossRefGoogle Scholar.

¹⁹ The well-known phrase, “competition in risk taking,” is from Schelling, Thomas C., Arms and Influence (New Haven:Yale University Press, 1966Google Scholar). This point is formally established in Morrow (fn. 17).

²⁰ For a formal discussion of this point and the link between the willingness to take risks in crises and prior alliance behavior, see Morrow, James D., “On the Theoretical Basis of a Measure of National Risk Attitudes,” International Studies Quarterly 31 (No. 4, 1987), 423CrossRefGoogle Scholar–38.

²¹ Hitler is said to have commented about what would have happened if France had resisted German demands in the Rhineland crisis: “We would have had to withdraw with our tails between our legs, for the military resources at our disposal would have been wholly inadequate for even a moderate resistance.” Cited in de Mesquita, Bruce Bueno, The War Trap (New Haven:Yale University Press, 1981), 173Google Scholar.

²² Plott (fn. 1, pp. 539–42) contends that if we treat lotteries as outcomes, this problem disappears because then changes in risk attitudes are changes in ordinal preferences over lotteries. But this line of logic has to violate either the sure-thing principle that leads to Von Neumann-Morgenstern cardinal utilities, or the conditions of unrestricted domain. See Savage, Leonard J., The Foundations of Statistics, 2d ed. (New York:Dover, 1972), 21–22Google Scholar, 99 100, for a definition and discussion of the sure-thing principle. If any set of ordinal preferences over lotteries is admissible, then one can prefer afifty-fiftylottery of winning or losing over winning for certain, which is preferred to losing for certain. Such a preference scheme clearly violates the sure-thing principle. Because the models discussed in the text assume Von Neumann-Morgenstern utility, they will violate the condition of unrestricted domain if lotteries are treated as outcomes.

²³ Gibbard, Allan, “Manipulation of Voting Schemes: A General Result,” Econometrica 41 (July 1973), 587–601CrossRefGoogle Scholar. Although Gibbard discusses manipulation in voting, his theorem applies to game forms, thereby covering social choice processes in general.

²⁴ See Waltz (fn. 9), and Gilpin, Robert G., War and Change in World Politics (New York:Cambridge University Press, 1981CrossRefGoogle Scholar).

²⁵ Waltz's argument that analysis must be conducted across multiple images runs parallel to the main thesis of this paper. The first and second images would be the source of preferences that, in conjunction with the structure of the third image, produce outcomes. See Waltz, Kenneth N., Man, the State, and War (New York:Columbia University Press, 1959Google Scholar).

²⁶ Waltz (fn. 9), 162.

²⁷ Ibid., Table 8.1, p. 162.

²⁸ Ibid., 162.

²⁹ In fairness to Waltz, let us admit that he makes a distinction between a theory of international politics and a theory of foreign policy. The latter explains the specific actions of states, while the former explains systemic consequences stemming from systemic characteristics (ibid., 121–22). Waltz also realizes that knowledge of preferences is necessary for a theory of foreign policy (p. 174). In this sense, this essay agrees with Waltz's central thesis.

Even with an emphasis on systemic-level explanation, preference can be included in what Waltz calls a theory of international politics. Drawing on the economic analogy of which Waltz is so fond, aggregate demand for specific goods indicates the accumulated preferences of many actors. Aggregate demand is not structural because it rises and ebbs with individual demands. The characterization of aggregations of preferences in international politics depends upon the particular theory employed.

³⁰ Waltz (fn. 9), 166.

³¹ Altfeld, Michael F., in a discussion of the conditions for alliance formation, focuses on the trade-off between autonomy and security; see “The Decision to Ally: A Theory and a Test,” Western Political Quarterly 37 (December 1984), 523CrossRefGoogle Scholar–44. Security and autonomy can be thought of as capturing a state's evaluation of the relative desirability of preserving issues as compared to changing them; see Morrow (fn. 20).

³² Waltz (fn. 9), 168. Also, Waltz is unclear as to whether or not bipolarity makes systems more stable in the sense of being less likely to change their nature; he certainly seems to imply that.

³³ For this argument and its application to arguments about polarity, see de Mesquita, Bruce Bueno, “Theories of International Conflict: An Analysis and Appraisal,” in Gurr, Ted Robert, ed., Handbook of Political Conflict (New York:Free Press, 1980), 361Google Scholar–98.

³⁴ Stein, , “When Misperception Matters,” World Politics 34 (July 1982), 505CrossRefGoogle Scholar–26.

³⁵ Waltz never defines uncertainty or describes what a certain world would look like. I employ the definition of uncertainty used in decision theory—namely, that probabilities of future outcomes are unknown or meaningless; see Luce, R. Duncan and Raiffa, Howard, Games and Decisions (New York:John Wiley, 1957Google Scholar). This definition does not imply that future events are perfectly predictable when uncertainty is absent; rather, that future events have probabilities known to all, as is the case with games of chance.

³⁶ For a formalization of this argument, see Morrow (fn. 17).

³⁷ Waltz (fn. 9), 74–77, 127–28.

³⁸ Gibbard (fn. 23).

³⁹ Waltz (fn. 9), 127–28.

⁴⁰ Gilpin (fn. 24), 10.

⁴¹ Ibid., 14.

⁴² Ibid., 10.

⁴³ A different interpretation of Gilpin would suggest that disequilibrium is simply a change in the expected costs and benefits of challenging the original position of equilibrium, rather than an expected net benefit. In this case, equilibrium and disequilibrium would coexist in the system, and the presence of disequilibrium would not trigger a challenge. However, this approach also has problems beyond its strange use of contradictory terms—as will be seen below.

⁴⁴ Gilpin (fn. 24), 14–15.

⁴⁵ Ibid., 199–200.

⁴⁶ Ibid., 31.

⁴⁷ This approach allows the coexistence of equilibrium and disequilibrium, as discussed in fn. 43.

⁴⁸ For an excellent informal discussion of this point and its consequences, see Witt-man, Donald, “How a War Ends: A Rational Model Approach,” Journal of Conflict Resolution 23 (December 1979), 743CrossRefGoogle Scholar–63. Gilpin's expected net benefits for continuing to fight would be identified with Wittman's difference between expected utility of war and the utility of a negotiated settlement. See esp. pp. 749–51.

⁴⁹ Fischer, Fritz, Germany's Aims in the First World War (New York:Norton, 1967Google Scholar).

⁵⁰ I am indebted to Robert Axelrod for suggesting the possibility that strategic rationality leads to the accumulation of disequilibrium.

⁵¹ This observation parallels Bueno de Mesquita's point (fn. 33) that Organski's power transition theory requires challengers to be risk-acceptant and dominant states to be risk-averse. See Organski, A.F.K., World Politics, 2d ed. (New York:Knopf, 1968), 299–338Google Scholar, and Organski, A.F.K. and Kugler, Jacek, The War Ledger (Chicago:University of Chicago Press, 1980), 1–63Google Scholar, for the power transition theory.

⁵² To give credit to Gilpin, he seems to realize this problem. When he discusses the onset of hegemonic war, he tries to argue that the actors no longer act rationally (fn. 24, p. 202). But if the actors are rational before the onset of hegemonic war and avoid unprofitable conflict, should they not continue to do so after the outbreak of such a war?

⁵³ Ibid., 205.

⁵⁴ Ibid., 196–97. A thorough treatment of the development of the Anglo-German rivalry is given in Kennedy, Paul, The Rise of the Anglo-German Antagonism, 1860–1914 (London:Allen & Unwin, 1980Google Scholar).

⁵⁵ Gilpin (fn. 24), 199–203.

⁵⁶ I do not argue that I have been able to show why rational actors would expand a war for limited goals into a hegemonic war. Consequently, I cannot offer a complete explanation. Still, it seems to me that the critical questions are, why are all the major powers drawn into the struggle, and why do the issues at dispute expand to encompass all the issues? Expansion of a war to include most major powers seems essential to producing a hegemonic war. An insightful discussion of this point is given in Blainey, Geoffrey, The Causes of War (New York:Free Press, 1973), 196CrossRefGoogle Scholar–97.

⁵⁷ An excellent example of controlling for the strategic situation when determining preferences is given in Denzau, Arthur, Riker, William, and Shepsle, Kenneth, “Farquaharson and Fenno: Sophisticated Voting and Home Style,” American Political Science Review (December 1985), 1117CrossRefGoogle Scholar–34. The authors argue that members of Congress will sometimes vote their preferences and sometimes not, depending on their vulnerability in their home districts in the next election; they illustrate the argument by reference to the Powell amendment to a 1956 bill providing federal aid to education.

⁵⁸ See Oye, Kenneth A., ed., Cooperation under Anarchy (Princeton:Princeton University Press, 1986Google Scholar), for an example of the current interest in game theory as a model in several fields of world politics.

⁵⁹ Duncan Snidal, “The Game Theory of International Politics,” ibid., 25–57.

⁶⁰ One of the successes of Bueno de Mesquita (fn. 21) is the estimation of national preferences from one set of prior decisions-alliance commitments. Although the theoretical basis of this measure is not fully specified, the argument that alliance commitments reveal a state's preferences for other states’ policies seems plausible.

⁶¹ An ambitious attempt to deal with this problem is presented in de Mes-quita, Bruce Bueno, Newman, David, and Rabushka, Alvin, Forecasting Political Events: The Future of Hong Kong (New Haven:Yale University Press, 1985Google Scholar).