I am very grateful to S. N. Eisenstadt and Harold Saunders for their generous assistance in providing insight into Middle Eastern affairs and for providing the data for this project. I am also grateful to I. William Zartman for his instrumental role in stimulating research on multilateral negotiations and to the United States Institute of Peace for its support and encouragement of research on multilateral negotiations. James Morrow provided much helpful assistance. Any errors, of course, are my own.

1. A Condorcet winner is an alternative which in a complete set of pairwise comparisons defeats each other alternative and is never itself defeated. For an elaboration of the difficulties inherent in multilateral negotiations, see Zartman, I. William, “Many Are Called but Few Choose: Managing Complexity in Multilateral Negotiations,” working paper series WP-14, Johns Hopkins University School of Advanced International Studies, Baltimore, Md., 1988Google Scholar.

2. See Schwartz, Thomas, “No Minimally Reasonable Collective-Choice Process Can Be Strategy-Proof,” Mathematical Social Sciences 3 (01 1982), pp. 57–72Google Scholar. If time and information are scarce and if preferences are not cyclic, then trades may be effective. In such cases, we may profit from an examination of the manipulation of information through the bargaining or signalling process. See Banks, Jeffrey and Sobel, Joel, “Equilibrium Selection in Signalling Games,” Econometrica 55 (07 1982), pp. 647–61Google Scholar.

3. Convexity merely requires that if any point (or possible outcome of a negotiation) α is included in the set of feasible outcomes and if any other point (or possible outcome) β is also in the feasible set, then all points on the straight line that connects α to β are also within the feasible set of outcomes.

4. See McKelvey, Richard, “Intransitivities in Multidimensional Voting Models and Some Implications for Agenda Control,” Journal of Economic Theory 12 (06 1976), pp. 472–82Google Scholar; McKelvey, Richard, “General Conditions for Global Intransitivities in Formal Voting Models,” Econometrica 47 (09 1979), pp. 1085–112Google Scholar; Schofield, Norman, “Instability of Simple Dynamic Games,” Review of Economic Studies 45 (10 1976), pp. 575–94Google Scholar; and Ordeshook, Peter, Game Theory and Political Theory (New York: Cambridge University Press, 1986)Google Scholar.

5. See McKelvey, “General Conditions for Global Intransitivities in Formal Voting Models”; and Schofield, “Instability of Simple Dynamic Games”.

6. See the following articles by Shepsle, Kenneth and Weingast, Barry: “Structure-Induced Equilibrium and Legislative Choice,” Public Choice, vol. 37, no. 3, 1981, pp. 503–19Google Scholar; and “The Institutional Foundations of Committee Power,” American Political Science Review 81 (03 1987), pp. 85–104Google Scholar.

7. For a discussion of anarchy in the international system, see Waltz, Kenneth, “The Origins of War in Neorealist Theory,” in Rotberg, Robert and Rabb, Theodore, eds., The Origin and Prevention of Major Wars (Cambridge: Cambridge University Press, 1988), pp. 39–52Google Scholar. For further discussion of the applicability of the social choice literature to international relations, see Morrow, James D., “Social Choice and System Structure in World Politics,” World Politics 41 (10 1988), pp. 75–97Google Scholar.

8. de Mesquita, Bruce Bueno, Rabushka, Alvin, and Newman, David, Forecasting Political Events: The Future of Hong Kong (New Haven, Conn.: Yale University Press, 1985)Google Scholar.

9. See Black, Duncan, Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958)Google Scholar; and Downs, Anthony, An Economic Theory of Democracy (New York: Harper & Row, 1957)Google Scholar. See also de Mesquita, Bruce Bueno, “Forecasting Policy Decisions: An Expected Utility Approach to Post-Khomeini Iran,” PS 17 (Spring 1984), pp. 226–36Google Scholar; Morrow, James, “A Spatial Model of International Conflict,” American Political Science Review 80 (12 1986), pp. 1131–50Google Scholar; Morgan, T. Clifton, “A Spatial Model of Crisis Bargaining,” International Studies Quarterly 28 (12 1984), pp. 407–26Google Scholar; Morgan, T. Clifton, “Power, Resolve and Bargaining in International Crises: A Spatial Theory,” International Interactions, vol. 15, nos. 3 and 4, 1989, pp. 289–312Google Scholar; and Morgan, T. Clifton, “Issue Linkages in International Crisis Bargaining,” American Journal of Political Science 34 (05 1990)Google Scholar.

10. Such an actor neither needs complete information nor needs to examine all alternatives. See Harsanyi, John, Rational Behavior and Bargaining Equilibrium in Games and Social Situations (Cambridge: Cambridge University Press, 1977)Google Scholar; Selten, Reinhart, “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory, vol. 4, no. 1, 1975, pp. 25–55Google Scholar; Kreps, David and Wilson, Robert, “Sequential Equilibria,” Econometrica 50 (07 1982), pp. 863–94Google Scholar; and Cho, In-koo and Kreps, David, “Signaling Games and Stable Equilibria,” Quarterly Journal of Economics 102 (05 1978), pp. 179–222Google Scholar. For examples in international relations, see Alt, James, Calvert, Randall, and Humes, Brian D., “Reputation and Hegemonic Stability,” American Political Science Review 82 (06 1988), pp. 445–66Google Scholar; Powell, Robert, “Crisis Bargaining, Escalation, and MAD,” American Political Science Review 81 (09 1987), pp. 717–35Google Scholar; Morrow, James D., “Capabilities, Uncertainty and Resolve,” American Journal of Political Science 33 (11 1989), pp. 941–72Google Scholar; and de Mesquita, Bruce Bueno and Lalman, David, “Domestic Opposition and Foreign War,” American Political Science Review 84 (09 1990)Google Scholar.

11. Black, The Theory of Committees and Elections.

12. The model here is not game theoretic. It does, however, contain a rational expectations component that looks at anticipated courses of action in the event that a group does not challenge a policy proposal. Decision theoretic models with such components tend to converge on game theoretic equilibria. See the following working papers of Marcet, Albert and Sargent, Thomas: “The Fate of Systems with ‘Adaptive Expectations’” and “Convergence of Least Squares Learning in Environments with Hidden State Variables and Private Information,” mimeographs, Hoover Institution, 11 and 12 1987Google Scholar. For a game theoretic treatment of problems related to those investigated here, see the following works of de Mesquita, Bruce Bueno and Lalman, David: “Domestic Opposition and Foreign War”; “The Road to War Is Strewn with Peaceful Intentions,” in Ordeshook, Peter, ed., Models of Strategic Choice in Politics (Ann Arbor: University of Michigan Press, 1989), pp. 253–66Google Scholar; and War and Reason (New Haven, Conn.: Yale University Press, forthcoming).

13. de Mesquita, Bruce Bueno and Lalman, David, “Reason and War,” The American Political Science Review 80 (12 1986), pp. 1113–31CrossRefGoogle Scholar. The measurement of the probability of success for i's preferred outcome in a competition with j's preferred outcome is accomplished using the following specification:

with p denoting preference and with utilities (Uterms) and saliences (S terms) in V^k defined as described below.

14. See de Mesquita, Bruce Bueno, “The War Trap Revisited,” American Political Science Review 79 (03 1985), pp. 157–76Google Scholar. For further discussion of the measurement of risk, see Morrow, James D., “On the Theoretical Basis of a Measure of National Risk Attitudes,” International Studies Quarterly 31 (12 1987), pp. 423–38Google Scholar.

15. See Bueno de Mesquita and Lalman, “Reason and War”.

16. Ibid..

17. Keohane, Robert, After Hegemony (Princeton, N.J.: Princeton University Press, 1984)Google Scholar.

18. For a detailed example (drawn from Italian politics) of such an application of the model, see Beck, Douglas and de Mesquita, Bruce Bueno, “Forecasting Policy Decisions: An Expected Utility Approach,” in Andriole, S., ed., Corporate Crisis Management (Princeton, N.J.: Petrocelli Books, 1985), pp. 103–22Google Scholar.

19. Professor Eisenstadt, who has been very helpful in the development of this analysis, is not responsible for the conclusions and inferences drawn from the model. The principal purpose in applying these data is to illustrate how the techniques outlined here can be used and not to undertake an in-depth assessment of the prospects for peace in the Middle East. However, it should be evident that such a detailed assessment could be accomplished if this model were combined with the subtle understanding only possessed by an area expert.

20. Those not familiar with the model being utilized here may well wonder about the reliability of any process that relies on so small a sample of sources of critical information. However, it must be borne in mind that the method applied here is mathematical, not statistical, and the information required of the experts is basic and fundamental. In controlled experiments, it has been found that the correlation in model results across different expert sources of information is well over.90. That is, different experts may disagree about expected outcomes on issues and they may organize information differently so that inputs appear to be different, but their inputs to the model almost always yield the same output predictions from the model. This is because knowing who the players are on an issue, what their preferred outcome is, what their relative influence is, and how important the issue is to them is fundamental to being an expert on the sorts of issues examined using this methodology.

21. The New York Times, 7 June 1988, p. 1.

22. This sentence was written in the summer of 1988. Since that time, the United States has successfully pressured Arafat to recognize Israel's right to exist, a recognition which the PLO previously refused.