The article develops an expected-utility model of extended deterrence and tests it on 54 historical cases. Successful deterrence is associated with close economic and political ties between the defender and the state it is trying to protect, and with a local military balance in favor of the defender. Deterrence success is not systematically associated with the presence of a military alliance, with the overall strategic military balance, with possession of nuclear weapons, or with the defender's firmness or lack of it in previous crises. If deterrence fails, only alliance and the military value of the state under attack are associated with the defender's willingness to go to war.
1 Deterrence: A Conceptual Analysis, 2d ed. (Beverly Hills: Sage, 1983) 11.
2 Morgan (fn. 1), 30.
3 Russett, Bruce, “The Calculus of Deterrence,” Journal of Conflict Resolution 7 (March 1963), 97–109. The logic of this analysis was extended, and difficulties in comprehending the reasons for success and failure delineated further, in Russett, Bruce, “Pearl Harbor: Deterrence Theory and Decision Theory,” Journal of Peace Research 4 (No. 2, 1967), 89–105.
4 Morgan (fn. 1), 38. Morgan also used a fourth criterion requiring that the leaders of the attacker state desist primarily because of the retaliatory threat. Such a judgment cannot be made definitively. But in all the cases that met our other criteria, we are satisfied that a failure to attack was largely because of the defender's threat.
5 See especially the argument in Mesquita, Bruce Bueno de, The War Trap (New Haven: Yale University Press, 1981), 27–29.
6 Decisions to threaten a smaller state with attack usually are the result of substantial premeditation (resulting from previously perceived opportunities or provocations), even when they are triggered by a short-term crisis. Similarly, decisions to counter such a threat are usually (though less often) presaged by deliberation or contingency planning.
7 Schelling, Thomas C., The Strategy of Conflict (Cambridge, Harvard University Press, 1960), 3–20.
8 Formally, the attacker will fight if Ua1 (p) + Ua2 (1 − p) > U, where Ua3 is the utility of attacking if the defender resists, Ua2 is the utility of attacking if the defender does not resist, Ua3 is the utility of no attack, and p is the attacker's subjective probability that the defender will resist. If the defender had full freedom of action to decide whether to resist or not only after attacker had committed himself, the utility calculation would be simple: fight only if U1a > U1b, where U1a is the utility of resisting an attack and U1b the utility of not resisting. But since much of deterrence consists in committing oneself to irreversible acts (with which one might in the end wish one did not have to follow through), the defender too must calculate from the beginning the probability that the attacker will indeed attack, and the defender's own utilities from the “attacker's” nonattack (if deterrence succeeds) as well as from attack. Hence the symmetrical formula for the defender in deciding whether to commit himself to fight: U12(q) + U12 (1 − q) > U13 where q is the probability that deterrence will fail. In deciding on the probability the other will fight, each must estimate the other's utilities. In doing so each must make some judgment about whether the other is risk-averse or risk-acceptant. We include a measure for that element in the analysis below. This presentation assumes cardinal calculations of utility and probability; of course few if any political decision-makers attach such firm calculations to decisions they make. Nevertheless a rational decision-maker has to operate in some crude approximation of this fashion, with estimates of more and less, and our ultimate conclusions do not depend on our assumption being a perfect representation of reality.
9 The systematic evidence on this point is against attributing great importance to the military balance. Weede, Erich, “Extended Deterrence by Superpower Alliance,” Journal of Conflict Resolution (June 1982), 231–54, reports evidence that mutual nuclear deterrence prevents war not only between the superpowers, but between their allies across the alliance divide. Organski, A.F.K. and Kugler, Jacek, The War Ledger (Chicago: University of Chicago Press, 1980), chap. 4, find nuclear powers prevailed in only about half of the deterrence crises studied, though local conventional superiority did seem to help. Kugler, Jacek, “Terror without Deterrence,” Journal of Conflict Resolution 28 (September 1984), reports similar results, and that even nuclear monopoly (much less if both powers have a nuclear option) brought a favorable outcome only half the time. Russett, , “Calculus of Deterrence” (fn. 3), reports the irrelevance of both conventional and strategic superiority, and both he and Bueno de Mesquita (The War Trap, fn. 5, chap. 5) report the inferior predictive power of the military balance as compared with a full expected-utility model. Siverson, Randolph and Tennefoss, Michael, “Alliance, Power, and the Escalation of Conflicts: 1815–1965,” mimeo. (Davis: University of California, 1982), find that minor powers with major-power allies are less likely to be the targets of threat than are minor powers without such allies, and that minor powers with major-power allies are less likely to have those threats escalate to war. Nevertheless, all these studies (least The War Trap) suffer from challengeable decisions about case selection or measurement, and the results are hardly definitive. More broadly in the literature, there is some evidence that wars are more likely between states of near-equal power than between states of very disparate power. But it is still not clear whether that statement merely says that states very different in power are unlikely to go to war (they don't “need” to, because it is clear who would win), and whether the war-among-near-equals phenomenon is really a result of changing power relationships in the region of near equality. On this see Russett, Bruce and Starr, Harvey, World Politics: The Menu for Choice (San Francisco: W. H. Freeman, 1981), 119.
10 George, Alexander and Smoke, Richard, Deterrence in American Foreign Policy (New York: Columbia University Press, 1974), 52.
11 This is not to imply that it will have the same value on both sides of the equation, only that a more valuable protégé will have greater value on both sides than would a less valuable protégé. Western Europe is a case in point. Presumably its value is much greater (prosperous, industrially intact, willingly allied) to the Western alliance than it would be (economically chaotic, devastated, sullenly occupied) to the Soviet side after a successful Soviet attack. Nevertheless, we imagine that Western Europe is of sufficient intrinsic value that the Soviet Union might under some circumstances pay costs to acquire it that it would never pay to acquire, say, only Finland.
12 See MichaelAltfeld, and Mesquita, Bruce Bueno de, “Choosing Sides in Wars,” International Studies Quarterly 23 (March 1979), 87–112. For a good discussion on the matter of deriving generalizations from a deterrer's past behavior, versus the context-bound meaning of the behavior, see Jervis, Robert, “Deterrence and Perception,” International Security 7 (Winter 1982/1983), 3–30, esp. 8–13.
13 Tillema, H. K. and Wingen, J. R. Van, “Law and Power in Military Interventions by Major States after World War II,” International Studies Quarterly 26 (June 1982), 220–50, report that ties of formal alliance, and defender's military bases on the territory of the protégé are associated with successful deterrence. Russett, , “Calculus of Deterrence” (fn. 3), found no such association with alliance but did with various ties of economic and political interdependence and military cooperation. Russett, Bruce and Nincic, Miroslav, “American Opinion on the Use of Military Force Abroad,” Political Science Quarterly 91 (Fall 1976), 411–32, report that among the general American public, willingness to aid other states militarily is stronger the greater the geographical proximity of the protégé and the level of foreign trade. Neither formal alliance nor similarity of political system (save for the protégé's not having a communist government) seemed to matter much.
14 This classification is taken from Gochman, Charles and Maoz, Zeev, “Serious Interstate Disputes, 1816–1976: Empirical Patterns and Theoretical Insights,” journal of Conflict Resolution 28 (forthcoming, 1984).
15 The full data set with all variables is available from the authors. The sources used to identify and select cases of attempted deterrence were Small, Melvin and Singer, J. David, Resort to Arms (Beverly Hills: Sage, 1982); Siverson, Randolph and Tennefoss, Michael, “Interstate Conflicts: 1815–1965,” International Interactions 9 (July 1982), 147–78, particularly the appendix listing the data for the article; Snyder, Glenn and Diesing, Paul, Conflict Among Nations (Princeton: Princeton University Press, 1977), particularly the case summaries in the appendix, 531–70; George and Smoke (fn. 10), 105–500; Butterworth, Robert, Managing Interstate Conflict 1945–1975 (Pittsburgh: University Center for International Studies, 1976; Keesing's Contemporary Archives (London: Keesing's Ltd., 1933–1980); Index to The New York Times (New York: The New York Times, 1900–1980); Ehrlich, Thomas, Cyprus 1958–1967: International Crises and the Role of Law (New York and London: Oxford University Press, 1974); Quandt, William B., Decade of Decisions: American Policy Toward the Arab-Israeli Conflict 1967–1976 (Berkeley: University of California Press, 1977; Krosby, H. Peter, Finland, Germany, and the Soviet Union, 1940–1941—The Petsamo Dispute (Madison: University of Wisconsin Press, 1968); and the Correlates of the War Project data set on international disputes, 1816–1980, obtained from tapes made available through the Interuniversity Consortium for Political and Social Research at the University of Michigan. In some other candidate cases we decided either that there was no overt threat by the attacker (e.g., Soviet Union against Iran in 1979), or no previous overt deterrent threat by the deterrer (e.g., United States for South Korea before the North Korean attack, or the United Kingdom over the Falklands/Malvinas before the Argentine invasion). On this last case, see Lebow, Richard Ned, “Miscalculation in the South Atlantic: The Origins of the Falkland War,” Journal of Strategic Studies 6 (March 1983), 5–35. Inevitably a few cases are marginal for one reason or another. Probably the most questionable to many readers will be the characteri-
19 The raw data for the construction of this variable were obtained from tapes made available through the Interuniversity Consortium for Political and Social Research at the University of Michigan. For the development of the composite national capabilities index, see Singer, J. D., Bremer, S., and Stuckey, J., “Capability Distribution, Uncertainty, and Major Power War, 1820–1965,” in Russett, Bruce, ed., Peace, War and Numbers (Beverly Hills: Sage, 1972).
20 The formula used was that developed by Mesquita, Bueno de, The War Trap (fn. 5), 105. The function is a nonlinear one; i.e., the rate at which power declines is less over greater distances.
21 Data on military alliances were gathered from Russett, Bruce, “An Empirical Typology of International Military Alliances,” Midwest Journal ofPolitical Science 15 (May 1971), 262–80; Singer, J. David and Small, Melvin, “Formal Alliances, 1815–1939,” Journal of Peace Research 3 (No. 1, 1966), 1–32; and International Institute for Strategic Studies, The Military Balance (London: International Institute for Strategic Studies, 1961–1976).
22 Sources used to calculate trade shares were: SirScott-Keltle, John, ed. The Statesman's Yearbook (London: Macmillan, 1905–1910); Memorandum on International Trade and Balance of Payments (Geneva: League of Nations, 1910–1939); Mitchell, H. R., European Historical Statistics 1750–1970 (New York: Columbia University Press, 1975); Statistical Abstract of the United States (Washington D.C.: U.S. Government Printing Office, 1946–1950); Yearbook of International Trade Statistics (New York: United Nations, 1950–1980); World Tables 1976 (Baltimore: The Johns Hopkins University Press, 1976); Eckstein, Alexander, Galenson, Walter, and Liu, Ta-Chung, eds., Economic Trends in Communist China (Chicago: Aldine, 1969), 671–738; and Communist China's Balance of Payments (Washington, D.C.: Central Intelligence Agency, 1966).
23 Sources included Harkavy, Robert E., The Arms Trade and International Systems (Cambridge: Ballingerp, 1975); Stockholm International Peace Research Institute, SIPRI Yearbook (New York: Humanities Press, 1969–1980), U.S. Arms Control and Disarmament Agency, World Military Expenditures and Arms Transfers (Washington, D.C.: U.S. Government Printing Office, 1965–1980); U.S. Central Intelligence Agency, Communist Aid Activities in Non-Communist Less Developed Countries, 1954–1979 (Washington, D.C.: U.S. Government Printing Office, 1980); League of Nations, Statistical Yearbook of the Trade in Arms, Ammunition, and Implements of War (Geneva: League of Nations, 1924–1939); League of Nations, Armaments Yearbook (Geneva: League of Nations, 1923–1939); Kobayashi, Ushisaburo, War and Armament Loans of Japan (New York: Oxford University Press, 1922); Anderson, Eugene, The First Moroccan Crisis: 1904–1906 (Hamden, Conn.: Archon Books, 1966); Jean-Claude, Allain, Agadir: 1911 (Paris: Sorbonne, 1976); Kazemzadeh, Firuz, Russia and Britain in Persia, 1864–1914 (New Haven: Yale University Press, 1968); Thaden, Edward, Russia and the Balkan Alliance of 1912 (University Park: Pennsylvania State University Press, 1965); Tang, Peter S. M., Russia and Soviet Policy in Manchuria and Outer Mongolia (Durham, N.C.: Duke University Press, 1959). If there was more than one defender all defenders' military capabilities were included, but linkages were measured from the protégé to the defender that took the diplomatic lead in trying to deter.
24 In fact, all but one of the results we used are at the .95 level or above. A level of .9 is lower than would be appropriate if we had the luxury of a larger number of cases. But here use of a high level would risk too great a chance of rejecting hypotheses that are basically supported (type II error). Significance levels are given for a one-tailed test where the hypothesis indicates the sign of the expected relationship.
25 “The War Trap Revisited,” American Political Science Review 79 (forthcoming, 1985).
26 With a t-test of 1.93 it would be significant at the .95 level with a one-tailed test, but, since its sign is the opposite of that which we hypothesized, the level (.9) appropriate to a two-tailed test is applicable.
27 Alone among our variables, there is some problem of collinearity among the various measures of capability. The indicator for local existing military capability nevertheless remains significant even when other power measures are added to the equation, and it is by far the strongest when each of the four capability measures is used alone.
28 This result also is a bit sensitive to the inclusion or exclusion of the case of Vietnam. If Vietnam were to be dropped, the probabilities, especially toward the upper range of defender's superiority, would be markedly higher.
29 It is worth noting that economic and military-political ties are probably among the variables for which we have the least satisfactory fit between theoretical concept and empirical indicator. If so, and the biasing effect is essentially random, then we may be understating their true predictive power. One instance (no. 49) in which our model erroneously predicted deterrence would fail almost surely results from a weakness in our measure of military strength. In common with most other such efforts (see Organski and Kugler, chap. 2 [fn. 9], our indicator underestimates Israel's capability.
30 Several articles make this point well. See Mack, Andrew, “Why Big Nations Lose Small Wars,” World Politics 27 (January 1975), 175–200; Mueller, John, “The Search for a ‘Breaking Point’ in Vietnam,” International Studies Quarterly 24 (December 1980), 497–519; and Jervis, Robert, “Bargaining and Bargaining Tactics,” in Pennock, J. Roland and Chapman, John W., eds., Coercion: NOMOS XIV (Chicago: Aldine, 1972).
31 Kennedy, Paul, The Realities Behind Diplomacy: Background Influences in British External Policy, 1865–1980 (London: Allen Unwin, 1981).
32 The Evolution of Nuclear Strategy (New York: St. Martin's, 1981), XV.
33 In broad outline these results confirm the earlier conclusions of Russett, “Calculus of Deterrence” (fn. 3). They also support George and Smoke's finding (fn. 10) that the attacker's perception of the adequacy and appropriateness of the defender's military capability is neither a sufficient nor an adequate condition for successful deterrence.
* For comments and assistance we want to thank Robert Axelrod, Roy Behr, Bruce Bueno de Mesquita, Mark Hanson, Robert Jervis, Paul Kennedy, Jeffry Klugman, Ed Lazarus, Richard Ned Lebow, Patrick Morgan, Yoshitaka Nishizawa, Steven Rosenstone, and Yagil Weinberg, without attributing to them any responsibility for our errors.
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