¹ For other definitions of the term, and applications of paradoxical logic to the study of political phenomena, see Brams, Steven J., Paradoxes in Politics: Introduction to the Nonobvious Political Science (New York:Free Press, 1976Google Scholar); Maydole, Robert E., “Superpower Paradoxes” (mimeo., Davidson College, 1987Google Scholar); Quine, W. V., The Ways of Paradox (New York:Random House, 1965Google Scholar); Bose, Arun, Political Paradoxes and Puzzles (Oxford:Clarendon Press, 1977Google Scholar); Luttwak, Edward N., Strategy (Cambridge, MA:Belknap Press, 1987Google Scholar).

² For a thoughtful discussion of these meanings of the term, see Hart, Jeffrey, “Three Approaches to the Measurement of Power in International Relations,” International Organization 30 (April 1976), 299–305CrossRefGoogle Scholar.

³ See, for example, Singer, J. David, Bremer, Stuart, and Stuckey, John, “Capability Distribution, Uncertainty, and Major Power War, 1820–1965,” in Russett, Bruce M., ed., Peace, War, and Numbers (Beverly Hills, CA:Sage, 1972), 19–48Google Scholar; Organski, A.F.K. and Kugler, Jacek, The War Ledger (Chicago:University of Chicago Press, 1980Google Scholar); de Mesquita, Bruce Bueno, The War Trap (New Haven:Yale University Press, 1981Google Scholar).

⁴ See Levy, Jack S., “Declining Power and the Preventive Motivation for War,” World Politics 40 (October 1987), 82–107CrossRefGoogle Scholar, for a review of the literature on this issue.

⁵ I am using voting-related examples for two reasons. First, voting resources and voting power (in terms of control over outcomes) are some of the most simple and straightforward concepts to measure. This is contrary to concepts such as military capabilities and national power where no universally accepted definitions or measures exist. Second, the theory of sophisticated voting developed in Farquharson, Robin, Theory of Voting (New Haven:Yale University Press, 1969Google Scholar) provides the most convenient setting to show the paradox of power in a manner that satisfies the three criteria mentioned above.

⁶ The monotonicity paradox was proved by Felsenthal, Dan S. and Maoz, Zeev in “A Comparative Analysis of Sincere and Sophisticated Voting Under the Approval and Plurality Procedures,” Behavioral Science 33 (April 1988), 116CrossRefGoogle Scholar–30. For the original version of the chairman paradox, see Farquharson (fn. 5). Additional versions of that paradox are discussed in Brams, Steven J., Felsenthal, Dan S., and Maoz, Zeev, “New Chairman Paradoxes,” in Diekman, Andreas and Mitter, Peter, eds., Paradoxical Effects of Social Behavior: Essays in Honor of Anatol Rapoport (Vienna:Physica Verlag, 1986), 243CrossRefGoogle Scholar–56, and Maoz, Zeev and Felsenthal, Dan S., “Self-Binding Commitments, the Inducement of Trust, Social Choice and the Theory of International Cooperation,” International Studies Quarterly 31 (June 1987), 177–200CrossRefGoogle Scholar.

⁷ Maoz and Felsenthal (fn. 6) and Felsenthal and Maoz (fn. 6) show that both the monoto-nicity paradox and the chairman paradox can be combinations of personal power paradoxes and collective choice paradoxes in which the outcomes induced by selection of greater resources are socially inferior to those induced by the selection of lesser resources.

⁸ Jervis, , Perception and Misperception in International Politics (Princeton:Princeton University Press, 1976), 144Google Scholar–81.

⁹ On the tendency to interpret intentions from capabilities in the context of deterrence, see Jervis, Robert, “Perceiving and Coping With Threat,” in Jervis, Robert, Ned Lebow, Richard, and Gross Stein, Janice, Psychology and Deterrence (Baltimore:The Johns Hopkins University Press, 1985), 13–33Google Scholar. Also see Janice Gross Stein, “Calculation, Miscalculation, and Conventional Deterrence,” ibid., 34–88, and “Deterrence and Reassurance,” paper presented to the committee on the contribution of the behavioral sciences to the prevention of nuclear war, National Research Council, 1987.

¹⁰ For a discussion of the types of paradoxes, see Maydole (fn. 1), 5, and Quine (fn. 1).

¹¹ Blainey, Jeoffrey, The Causes of War (New York:Free Press, 1973CrossRefGoogle Scholar).

¹² Mandel, Robert, “The Effectiveness of Gunboat Diplomacy,” International Studies Quarterly 30 (March 1986), 59–76CrossRefGoogle Scholar; Maoz, Zeev, Paths to Conflict: International Dispute Initiation, 1816–1976 (Boulder, CO:Westview Press, 1982Google Scholar); Maoz, Zeev, “The Expected Utility of International Conflict: Some Logical Traps and Empirical Surprises in ‘The War Trap’” (mimeo., University of Haifa, 1984Google Scholar); Maoz, Zeev, “Resolve, Capabilities, and the Outcomes of Interstate Disputes, 1816–1976,” Journal of Conflict Resolution 27 (June 1983), 195–225CrossRefGoogle Scholar; Wayman, Frank W., Singer, J. David, and Goertz, Gary, “Capabilities, Military Allocations, and Success in Militarized Disputes,” International Studies Quarterly 27 (December 1983), 497–515CrossRefGoogle Scholar.

¹³ See Mack, Andrew J., “Why Big Nations Lose Small Wars: The Politics of Asymmetric Conflict,” World Politics 27 (January 1975), 175–200CrossRefGoogle Scholar.

¹⁴ This kind of historical analysis follows what George, Alexander L. and McKeown, Timothy J., “Case Studies and Theories of Organizational Decision Making,” in Cou-lam, Robert and Smith, Richard, eds., Advances in Information Processing in Organizations, Vol. 2 (Greenwich, CT:JAI Press, 1985), 29–34Google Scholar, call the “congruence procedure.” The idea is that a theoretical framework postulates a set of expected outcomes in one or more cases, and the fit between the expected and the actual outcomes serves as a basis for the assessment of the framework.

¹⁵ This analysis is based on the following sources: Crampton, Richard J., Bulgaria, 1878–1918: A History (Boulder, CO:East European Monographs, distributed by Columbia University Press, 1983Google Scholar); Dakin, Douglas, The Unification of Greece, 1770–1923 (London:Ernest Benn, 1972Google Scholar); Dedijer, Vladimir et al., History of Yugoslavia (New York:McGraw Hill, 1974Google Scholar); Diplomatist (anonymous), Nationalism and War in the Near East (Oxford:Clarendon Press, 1915Google Scholar); Helmreich, Ernest C., The Diplomacy of the Balkan Wars, 1912–1913 (New York:Russell & Russell, 1969Google Scholar); Miller, William, The Ottoman Empire and Its Successors, 1801–1927 (London:Frank Cass, 1966Google Scholar); Petrovich, Michael Boro, A History of Modern Serbia, 1804–1918, Vol. II (New York:Harcourt Brace Jovanovich, 1976Google Scholar); and Trotsky, Leon, The Balkan Wars, 1912–1913 (New York:Monad Press, 1980Google Scholar).

¹⁶ The Balkan Wars also shed considerable light on what Bruce Bueno de Mesquita (fn. 3) considers a counterintuitive aspect of international politics: war among allies.

¹⁷ Works on international crises covering this period have generally ignored these two wars. For example, Snyder, Glenn and Diesing, Paul, Conflict Among Nations (Princeton:Princeton University Press, 1977Google Scholar) mention these wars only in passing, in the context of Great Power diplomacy (p. 433). Ned Lebow, Richard, Between Peace and War (Baltimore:The Johns Hopkins University Press, 1981Google Scholar) ignores these wars completely. For an exception, see the discussion of the series of crises leading to World War I that deals explicitly with the Balkan Wars in Ned Sabrosky, Alan, “From Bosnia to Sarajevo: A Comparative Discussion of International Crises,” Journal of Conflict Resolution 19 (March 1975), 3–24CrossRefGoogle Scholar.

¹⁸ Although Montenegro was another participant in the alliance systems leading to the First Balkan War, it will not be discussed for two reasons. First, it was the weakest link in the chain, its capabilities having little effect on the total balance of forces. Second, it was heavily under Serbian influence, rendering its independence of choice questionable.

¹⁹ The text of this proposal may be found in Helmreich (fn. 15), 130.

²⁰ Diplomatist (fn. 15), 192.

²¹ The Bulgarian army numbered some 600,000 troops (as opposed to 592,000 during the first war); the Greek army was reduced to 200,000 troops (from 215,000 during the war), and the Serbian army to 350,000 (from a total of over 400,000 during the war). These figures from Crampton (fn. 15), 417–20, generally agree with those in Petrovich (fn. 15), 603, who estimates the strength of the Romanian army at 437,000 troops and of the Turkish army at 255,000. Yet these numbers differ markedly from the estimates of the combined strength of the combatants in the First Balkan War given by other authors. Trotsky (fn. 15), 139–40, relying on a noted German military commentator, gives the size of the various armies at the start of the First Balkan War as follows: Bulgaria 200,000 (160,000 combatants); Serbia 120,000 (95,000 combatants); Greece 55,000 (45,000 combatants); Montenegro 35,000; Turkey 450,000 (360,000 combatants). These may be gross underestimates. On p. 272, Trotsky puts the total Bulgarian casualties in the First Balkan War at 102,000, suggesting that the size of the Bulgarian army was at least twice the initial estimate. Diplomatist (fn. 15), 176, cites an interview in Near East in the winter of 1911–1912 with a leading Young Turk, who estimated the mobilization capacity of the allies at 450,000 and the Turkish mobilization capacity at 800,000.

²² Following the two Balkan Wars, the Bulgarian balance sheet did show some surplus. However, it was not only much smaller than it had been at the end of the First Balkan War, but it registered the smallest relative gain of all the allies in the first war. Helmreich (fn. 15), 453, shows changes in territory and population as a result of the two Balkan Wars. According to his figures, Bulgaria's territory was expanded by nearly 29%, and its population by 3%. This compares to a territorial expansion of 67% and a demographic expansion of 63% of Greece; a territorial expansion of 61% and a demographic expansion of 100% of Montenegro; and a territorial expansion of 81% and a demographic expansion of 55% of Serbia.

²³ In fact, Helmreich, ibid., 350–51, reports that secret discussions between the two former enemies, Serbia and Turkey, took place throughout June 1913, in the best spirit of Realpolitik.

²⁴ Ibid., 359–62.

²⁵ Ibid., 363–67; Crampton (fn. 15), 424.

²⁶ Helmreich (fn. 15), 366–67. “Now, after your declaration [requesting Russia to state its position within ten days] I communicate ours to you! Do not expect anything from us, and forget the existence of any of our engagements from 1902 until today.” Quoted, ibid., 361.

²⁷ The discussion of Israel's misfortune in Lebanon is based on Rabinovich, Itamar, The War for Lebanon, 1970–1983, rev. ed. (Ithaca, NY:Cornell University Press, 1985Google Scholar); Sahliye, Emile F., The PLO after the Lebanon War (Boulder, CO:Westview Press, 1986Google Scholar); Schiff, Zeev and Yaari, Ehud, Israel's Lebanon War (New York:Simon and Schuster, 1984Google Scholar); and Yaniv, Avner, Dilemmas of Security: Politics, Strategy, and the Israeli Experience in Lebanon (New York:Oxford University Press, 1987Google Scholar). These books offer detailed interpretations of the war seen from both the Israeli perspective and the perspective of the other participants in the war. Maoz and Felsenthal (fn. 6) analyze the strategic process leading to Israel's decision to withdraw from Lebanon in 1985.

²⁸ Yaniv (fn. 27), 100–103.

²⁹ Yaniv, Avner, Deterrence Without the Bomb: The Politics of Israeli Strategy (Lexington, MA:D.C. Health, 1986), 196–200Google Scholar, provides a telling estimate of the balance of power in the region. Israel's defense outlays increased from $1.5 billion in 1980 to $8 billion in 1982. The combined military outlays of Egypt, Syria, and Iraq dropped from $6.4 billion in 1980 to $5.7 billion in 1982. The relative capabilities of Israel and Syria are measured in Maoz, Zeev, “The Evolution of Syrian Power,” in Maoz, Moshe and Yaniv, Avner, eds., Syria Under Assad: Domestic Constraints and Military Risks (London:Croom Helm, 1985), 78–80Google Scholar, using a modified version of the Correlates of War composite capabilities index (with GNP substituting for the traditional energy consumption and iron-steel production indicators of economic capabilities). According to these figures, Israel's capability in 1982 accounted for about 15% of the total capabilities of a reference group including Syria, Turkey, Egypt, Jordan, and Iraq. Syria, on the other hand, accounted for 7% of the combined capabilities of this reference group.

³⁰ Yaniv (fn. 27), 102–7.

³¹ A discussion of the calculations made by the various parties in Lebanon is in Maoz and Felsenthal (fn. 6), 193–96.

³² See, for example, Yaniv, Avner and Lieber, Robert, “Personal Whim or Strategic Imperative: The Israeli Invasion of Lebanon,” International Security 8 (June 1983), 117CrossRefGoogle Scholar–42.

³³ Werner Leinfellner, “The Prisoner's Dilemma and Its Evolutionary Iteration,” in Diekman and Mitter (fn.6), 135.

³⁴ See especially Bueno de Mesquita (fn. 3), on expected utility and conflict outcomes; Maoz (fn. 12, 1983), on resolve; Steven Rosen, “War Power and the Willingness to Suffer,” in Russett (fn.3), on willpower; and Baldwin, David A., “Power Analysis and World Politics: New Trends versus Old Tendencies,” World Politics 31 (January 1979), 161CrossRefGoogle Scholar–94, on suitability of resources to political and military objectives.

³⁵ Brams et al. (fn. 6), 253; Maoz and Felsenthal (fn. 6), 196–97.

³⁶ Brams, Steven J., Felsenthal, Dan S., and Maoz, Zeev, “Chairman Paradoxes Under Approval Voting,” in Eberlein, Gerald and Berghel, Hal, eds., Theory and Decision (Dordrecht, Holland:D. Riedel Publishing Company, 1987), 223Google Scholar–33, show that chairman paradoxes are independent of the choice procedure or the distribution of resources. Felsenthal and Maoz (fn. 6) show the same thing with regard to the monotonicity paradox.

³⁷ The extent to which a systemic perspective such as Waltz's provides a solid context to an analysis of power paradoxes depends on which of Waltz's arguments is taken as characteristic of a systems theory of international politics. If it is that “structures cause actions to have consequences they were not intended to have,” as he contends in Theory of International Politics (Reading, MA:Addison Wesley, 1979), 107Google Scholar, then I do not agree that this argument is applicable to the power paradox. However, if it is the assertion he makes in “Reflections on Theory of International Politics: Response to My Critics,” in Keohane, Robert O., ed., Neorealism and Its Critics (New York:Columbia University Press, 1986), 338Google Scholar, that “structure is not independent of the parts, the states as actors, but constantly interacts with them,” then such a perspective seems a reasonable theoretical context within which the rational explanation can be cast.

³⁸ Maoz and Felsenthal (fn. 6) discuss how a chairman can resolve the paradox without relinquishing his prerogative: by a credible self-binding commitment to break ties strategically for less preferred alternatives rather than for more preferred ones.

³⁹ Leinfellner (fn. 33), 135–36.

⁴⁰ See, for example, Keohane, Robert O. and Nye, Joseph S. Jr., Power and Interdependence: World Politics in Transition (Boston:Little, Brown, 1977Google Scholar); Mansbach, Richard W. and Vasquez, John, In Search of Theory: A New Paradigm for Global Politics (New York:Columbia University Press, 1981Google Scholar); Vasquez, John, The Power of Power Politics: A Critique (New Brunswick, NJ:Rutgers University Press, 1983Google Scholar); and various authors in Keohane (fn. 37).

⁴¹ Singer, J. David, “The Incompleat Theorist: Insight Without Evidence,” in Knorr, Klaus and Rosenau, James N., eds., Contending Approaches to International Relations (Princeton:Princeton University Press, 1969), 65–66Google Scholar.

⁴² Ray, James Lee and Vural, Ayase, “Power Disparities and Paradoxical Conflict Outcomes,” International Interactions 12 (June 1986), 316CrossRefGoogle Scholar.

⁴³ Organski and Kugler (fn. 3); see also Kugler, Jacek and Domke, William, “Comparing the Strength of Nations,” Comparative Political Studies 19 (March 1986), 39–70CrossRefGoogle Scholar.

⁴⁴ Ray, and Vural, (fn. 42), and Lee Ray, James, Global Politics, 3rd ed. (Boston:Houghton Mifflin, 1987), 164Google Scholar–77, offer a comprehensive review of this literature.