1. Such studies appear in the references to this paper.

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4. Many different specific statistical distributions might be consistent with this general relationship (cf. D. Wilkinson, Deadly Quarrels, Berkeley, CA: 1980; Horvath, W. J., ‘A statistical model for the duration of wars and strikes’, Behavioral Science, 13, 1968, 18–28CrossRefGoogle Scholar; H. K. Weiss, ‘Stochastic models for the duration and magnitude of a “deadly quarrel”’, Operations Research, 11 January/February 1963, 101–121; Richardson, op cit.). Further, wars may end randomly at a fixed mean rate per time increment, or the rate at which wars end may vary with each time increment. Thus, Leavitt tries to estimate transition probabilities at various stages of crisis (Leavitt, ‘Markov processes in international crises: an analytical addendum to an event-based simulation of the Taiwan Straits crisis’, in Experimentation and Simulation in Political Science, J. A. Laponce and P. Smoker, eds., Toronto: 1972).

5. Wittman, D., ‘How a war ends: a rational model approach’, Journal of Conflict Resolution 23, 4 (1979), 743–763.CrossRefGoogle Scholar

6. Recent studies on differential war propensity support such an idea (cf. Small, M. and Singer, J. D., Resort to Arms: International and Civil Wars, 1816–1960, Beverly Hills, CA: 1982Google Scholar. W. W. Davis, G. T. Duncan and R. M. Siverson, ‘The dynamics of warfare: 1816–1965’. Washington, D.C. Presented at the annual meeting of the American Political Science Association, 1977. Starr, Mimeo H., Coalitions and Future War: Dyadic Study of Cooperation and Conflict, Beverly Hills, CA: 1975.)Google Scholar

7. The nature of a country's threshold depends upon a variety of cultural, economic, political and historical considerations. Generally speaking, however, we should expect the threshold to be higher when the regime's political existence is at stake, if the war is fought on the combatant's own territory, if the enemy clearly struck first, etc.

8. Weiss (Note 4) elaborates how the distribution of Richardson's 19th and 20th century wars through time could be generated by a Markov process based on the assumption that ‘The probability that a war ends after x deaths have occurred and before death x + 1 depends only on x.’

9. Ibid., p. 105.

10. Allan, P. and Stahel, A. A., ‘Tribal guerrila warfare against a colonial power: analyzing the war in Afghanistan’, Journal of Conflict Resolution 27, 4 (1983), 690–617.CrossRefGoogle Scholar

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12. J. S. Levy and T. C. Morgan, ‘The frequency and seriousness of war: an inverse relationship?’ Seattle, Washington: Presented at the annual meeting of the International Studies Association/Western Region, 1983. Mimeo. Richardson, op. cit.

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15. H. Wittman, op. cit., 753.

16. In the language of event history analysis this would mean that the partial derivative of the hazard function for war termination with respect to marginal casualties is negative, while the partial derivative with respect to cumulative casualties is positive (cf. Tuma, Hannan and Groeneveld, L. P., ‘Dynamic analysis of event histories’, American Journal of Sociology 84 (1979), 820–854.)Google Scholar

17. There may also be time lagged effects. The cumulative casualties in one war may act to inhibit the initiation of a following war. At the same time, however, they may provide a precedent for even larger subsequent military efforts.

When [major powers] suffer military defeat, and pay a high price in battle deaths per month of war, they tend to avoid war for a long time, and the longer they wait, the more intense the next war experience will be.

(Singer and Cusack, ‘Periodicity, inexorability, and steersmanship in international war’, in (R. L. Merritt and B. Russett, eds.), From National Development to Global Community, London: 1980.)

18. Non-casualty resources may have a dynamic similar to but still separate from casualties. Thus, there may be interactive effects including trade-offs between resource elements.

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23. This, of course, is related to capability exhaustion, which we discussed earlier.

24. Interestingly, the predictability of war results may have declined in recent times. Singer, Bremer and Stuckey (’Capability distribution, uncertainty, and major power war, 1820–1965’, in (B. M. Russett, ed.), Peace, War and Numbers, Beverley Hills, CA: 1972) found that ‘from 1816 through 1910, starting a war ended in failure for the initiator in only about one-fifth of the cases; but from 1911 through 1965, this error rate was as high as three-fifths of all cases’ (K. W. Deutsch, ‘Quantitative approaches to political analysis: some past trends and future prospects’. In (H. R. Alker, Jr., K. W. Deutsch and A. H. Stoetzel, eds.), Mathematical Approaches to Politics, Amsterdam: 1973.)

25. Perhaps such an asymmetry helps explain the fact that, despite heavy losses, Hitler took his own life rather than admit defeat. A counter-example is provided, however, by the Japanese rulers near the end of World War II. Following the surrender of Italy and Germany, and the US use of the atomic bomb, they chose to surrender.

26. Beer, F. A., Peace Against War: The Ecology of International Violence (San Francisco: 1981)Google Scholar. Space does not permit a full discussion of the underlying literature and principles. Interested readers should consult the book, which contains a 60-page bibliography.

27. Weiss, op. cit. (note 4), pp. 101–102.

28. This hypothesis assumes that the probabilities that separate peace initiatives will succeed are independent. This assumption seems appropriate for a general statement, but may not necessarily always be the case in specific situations. On the positive side, the submission of a number of peace initiatives may increase the probability that the next will succeed. Or there may be a threshold effect. A certain number of attempts may be required to convince the other side that one is serious. Alternatively, a peace initiative taken at the wrong time, or in the wrong context, may fail so badly that it decreases the likelihood that the next one will succeed.

29. This dynamic obviously only works in some circumstances. In others, increasing inequality may provide incentives for losers to settle quickly.

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33. This formulation is illustrated by events in Russia during World War I. It is, however, not always true and the limiting conditions are not clear. Thus the Eisenhower election during the Korean War led to a cease fire, but was not demonstrably the result of class conflict. In Britain, at the beginning of World War II, the Chamberlain government fell and was replaced by one headed by Churchill This reflected a desire for a stronger policy rather than a weaker one.

34. Ben-Zvi, A., ‘The outbreak and termination of the Pacific war: a juxtaposition of American preconceptions’, Journal of Peace Research 15,1 (1978); 33–49CrossRefGoogle Scholar. Halperin, M. H., ‘War termination as a problem in civil-military relations’, Annals 392 (11, 1970) 86–95Google Scholar. Foster, J. L. and Brewer, G. D., ‘And the clocks were striking thirteen: the termination of war’, Policy Sciences 7,2 (1976) 225–243.CrossRefGoogle Scholar

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