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² Wright (fn. 1), 636.

³ Richardson (fn. 1), 3.

⁴ Richardson, Lewis F., “The Distribution of Wars in Time,” Journal of the Royal Statistical Society 107 (Parts III-IV, 1944), 247CrossRefGoogle Scholar.

⁵ Richardson (fn. 1), vii.

⁶ Small and Singer (fn. 1), 38.

⁷ Ibid., 210

⁸ Ibid., 218–19.

⁹ Singer and Small (fn. 1), 23, and Small and Singer (fn. 1) categorize Austria-Hungary (1816–1918), Prussia/Germany (1816–1870; 1871–1918; 1925–1945), Russia/Soviet Union (1816–1917; 1922-present), France (1816–1940; 1945-present), England (1816-present), Italy (1860–1943), Japan (1895–1945), China (1949-present), and the United States (1898-present) as members of the major-power system. For their list of major-power wars, see Singer and Small (fn. 1), 70.

¹⁰ Bueno de Mesquita (fn. 1), 101.

¹¹ Levy (fn. 1), 51.

¹² Ibid., 3. Levy identifies France (1495–1975), England/Great Britain (1495–1975), the Hapsburg Dynasty (1495–1519; 1519–1556; 1556–1918), Spain (1495–1519; 1556–1808), the Ottoman Empire (1495–1699), the Netherlands (1609–1713), Sweden (1617–1721), Russia/Soviet Union (1721–1975), Prussia/Germany/West Germany (1740–1975), Italy (1861–1943), the United States (1898–1975), Japan (1905–1945), and China (1949–1975) as “Great Powers.” See Ibid., 24–43.

¹³ Ibid., 51.

¹⁴ It In my calculations, I made the following adjustments: extra-systemic and civil wars were excluded from Small and Singer's data; only their list of interstate wars was employed. Civil and imperial wars were deleted from Wright's compilation; only the wars he classified as defensive and balance-of-power conflicts were utilized in the subsequent analysis. Richardson's data were not broken down because it was difficult to determine which “deadly quarrels” were (and were not) between nation-states. I am indebted to Joanne Gowa and an anonymous referee for pointing out the need to analyze these compilations with only interstate wars.

¹⁵ Singer and Small (fn. 1), 78–128, provide an analysis of the agreement between Richardson's, Wright's, and their own data. However, they are concerned with different measures of agreement than the one used in this study. They compute the “commonality in percentage terms by… divid[ing] the number of wars which [a pair of data sets] included by the number which either of them included, for the period covered by both studies.” Ibid., 78; emphasis in original. Their results indicate only moderate agreement between the lists, and the “commonality declines even further [when they] compute… the number of wars found in every one of the… lists… and divide by the total found in any one of them” during the time periods when the studies overlap. Ibid., 79; emphases in original.

However, when Singer and Small analyze “for each pair of studies, what percentage of the first's wars are also in the second's list, and what percentage of the second's wars are found in the first's list… the discrepancies are not nearly so great as they first appeared.” Ibid., 79. Although Singer and Small find evidence of some commonality among the compilations that they compare, Table 2 indicates that there is little correlation between the data sets used in this study. Even though a considerable percentage of wars may be common to a given pair of data sets, the non-common outbreak of wars in a particular year seems to reduce the correlation significantly. Thus, I believe that the present analysis is a useful supplement to Singer and Small's seminal work on this topic.

¹⁶ Richardson (fn. 1), 30.

¹⁷ Bueno de Mesquita's dating of the Russian Revolution is not considered because he does not include civil wars in his data. Small and Singer, on the other hand, list this conflict twice, once as an extra-systemic war and once as a civil war. (Fn. 1, pp. 311, 321.)

¹⁸ The Poisson distribution occurs under the following circumstances: (a) the probability that an event (in this case, a war) occurs in a short period of time is proportional to the length of the period; (b) the probability that more than one event occurs in any very short period of time is zero; (c) the events are independent of one another; (d) the probability that an event occurs in a short period of time does not depend on when the period begins. Regardless of whether these assumptions hold, the Poisson distribution may be a good approximation to the distribution of wars. If that is true, it is important to know since it is empirically useful. Knowledge of the probability distribution is obviously of use for purposes of prediction. (For an example of the usefulness of the Poisson distribution for major-power wars, see Figure 11.)

¹⁹ See Wright (fn. 1); Richardson (fns. 1 and 4); Singer and Small (fn. 1); Houweling and Kuné (Table 1, fn. b); and Moyal, J. E., “The Distribution of Wars in Time,” Journal of the Royal Statistical Society 112 (Part IV, 1949), 447Google Scholar.

²⁰ A Poisson process is not necessarily at work just because the data fit the Poisson distribution. Thus, a tight fit does not necessarily imply randomness. For example, Houweling and Kuné (Table 1, fn. b) find that Small and Singer's data do not follow a Poisson process although they are closely approximated by a Poisson distribution. Interestingly, they are not able to reject the hypothesis that a Poisson process is at work when they analyze Small and Singer's “international wars, excluding civil wars.” Ibid., 60. See Ibid, for a more complete discussion of this issue.

²¹ The following adjustments were made: (1) The three dyads in 1827 involving Great Britain, France, and Russia versus Turkey were aggregated into the Battle of Navarino Bay. (2) The eight dyads that Bueno de Mesquita identifies in 1866 between Germany and eight states are aggregated into either the Seven Weeks' War or the Austro-Prussian War. (3) In both 1906 and 1907, Bueno de Mesquita lists two dyads that Wright aggregates into the Central American War; Small and Singer list one war between the combatants each year. I shall adopt the latter position as a compromise between Bueno de Mesquita, Wright, and Small and Singer. (4) The two dyads that appear in 1913 between Yugoslavia and Bulgaria, and Greece and Bulgaria were lumped together into the Second Balkan War to conform with the other scholars. (5) The five dyads in 1948 are aggregated into one war in Palestine to conform with both Richardson and Small and Singer. (6) The two dyads in 1965 between North Vietnam and both South Vietnam and the United States were condensed into one war, consistent with Small and Singer (the only other study including wars as recent as this one). (7) The three dyads in 1967 between Israel and Egypt, Syria, and Jordan, respectively, were aggregated into the Six-Day War. (8) The two dyads in 1973 between Israel and both Egypt and Syria were aggregated into the Yom Kippur War. Adjustments (7) and (8) are also in accord with Small and Singer's compilation.

²² Richardson (fn. 1), 141, and Small and Singer (fn. 1), 132. In earlier research, Small and Singer argue that not only is there “no long range secular trend” in the data as a whole, but that there is also no clear trend in the separate compilations of international wars, military confrontations, and civil wars, respectively. Small, Melvin and Singer, J. David, “Conflict in the International System, 1816–1977: Historical Trends and Policy Futures,” in Singer, J. David, ed., Understanding War (Beverly Hills, CA: Sage Publications, 1979)Google Scholar; Understanding War (Beverly Hills, CA: Sage Publications, 1979), 73Google Scholar.

²³ It should be noted that ordinary least-squares regression is a somewhat rudimentary technique for analyzing trends in data. It is frequently used for this purpose, however, and is the natural starting point in a comparative study of this sort. See, for example, Small and Singer (fn. 1); Levy (fn. 1); and Richardson (fn. 1).

²⁴ The use of tests of statistical significance is appropriate when a researcher is analyzing a sample and wants to generalize from the sample to the population. Such tests are inappropriate when the population is being studied. The data sets that are being used in this analysis can be thought of as the population of all wars during the time frames that each compilation covers. However, these data can also be considered a sample of the hypothetical population of all wars over all times. Tests of significance are often used in this paper, but, depending upon the assumptions that are made about the data, these tests may or may not be meaningful.

²⁵ In fact, Small and Singer have found that, when their subset of data on international wars is normalized to account for the number of nations in the international system, a “discernible downward trend” appears (fn. 22, p. 64). It is important to note that the decision to normalize or not to normalize these compilations “rests on an implied null model: that system size, population growth, or number of possible pairs, etc., should have no effect on the incidence of violence and conflict.” Ibid., 72; emphasis in original.

²⁶ The regression coefficients are quite small for each data set. However, it is possible that over the course of hundreds of years, the average number of wars could go up by a significant amount. Consequently, the percentage change was calculated between the predicted number of wars at the beginning of the time period and that at the end. The change exceeded 20% only in the case of Wright's data for all wars; however, in the latter case the change was approximately 70%, which is quite substantial.

²⁷ Houweling and Kuné (Table 1, fn. b); Moyal (fn. 19).

²⁸ Ibid., 447.

²⁹ If the value of a time series at time t is correlated with its value k periods before, the time series exhibits serial correlation (also known as autocorrelation). The assumption in classical linear regression is that there will be no serial correlation of the residuals. For present purposes, I am interested in whether the residuals are serially correlated because if they are, this might help us predict and understand the incidence of war.

³⁰ This is true if we use the standard table of the Durbin-Watson statistic and let n = 100. Alternatively, we can use the von Neumann ratio, which is n/(n — 1) multiplied by the Durbin-Watson statistic. Since for large n it may be taken as approximately normally distributed (its mean being 2n/(n — 1) and its variance being 4n ²(n — 2)/(n + 1)(n — 1)³), we can use this statistic to test for serial correlation of the residuals. In no case is the result statistically significant. For a more detailed explanation of this method, see J. Johnston, Econometric Methods, 2d ed. (New York: McGraw-Hill, 1972), 250–51.

³¹ Kondratieff identified a series of cycles in the international economy. Specifically, he argued that long waves existed in the wholesale price level, interest rates, wages, turnover in foreign trade, and the production and consumption of certain raw materials. Other researchers have found evidence of long cycles in investment, innovation, and profit levels. See Goldstein, Joshua S., “Kondratieff Waves as War Cycles,” International Studies Quarterly 29 (December 1985), 411–44CrossRefGoogle Scholar, for a discussion of this literature. Of particular interest for my purpose is Kondratieff s assertion that “it is during the period of the rise of long waves… that, as a rule, the most disastrous and extensive wars and revolutions occur.” See Kondratieff, Nikolai D., “Long Waves in Economic Life,” Review II (Spring 1979), 536Google Scholar (originally published as “Die langen Wellen der Konjunktur,” in Archiv für Sozialwissenschaft und Sozialpolitik LVI, No. 3, 1926Google Scholar.) Kondratieff speculated that the explanation for this finding may be that “wars originate in the acceleration of the pace and the increased tension of economic life, in the heightened economic struggle for markets and raw materials, and… social shocks happen most easily under the pressure of new economic forces.” Ibid., 539.

³² Thompson, William A. and Zuk, L. Gary, “War, Inflation, and the Kondratieff Long Wave,” Journal of Conflict Resolution 26 (December 1982), 621–44CrossRefGoogle Scholar.

³³ Goldstein (fn. 31), 424.

³⁴ Väyrynen, Raimo, “Economic Cycles, Power Transitions, Political Management and Wars Between Major Powers,” International Studies Quarterly 27 (December 1983), 389–418CrossRefGoogle Scholar.

³⁵ Thompson and Zuk (fn. 32).

³⁶ The causal connections between economic fluctuations and warfare (in both directions) remain ambiguous. Although these findings are interesting and potentially useful theoretically, one must be careful to distinguish between causality and correlation.

³⁷ Gilpin, Robert, The Political Economy of International Relations (Princeton: Princeton University Press, 1987)CrossRefGoogle Scholar; The Political Economy of International Relations (Princeton: Princeton University Press, 1987), 56Google Scholar, 57.

³⁸ See Krasner, Stephen D., “State Power and the Structure of International Trade,” World Politics 28 (April 1976), 317–47CrossRefGoogle Scholar. By increasingly “open” trading systems, Krasner is referring to those in which “tariffs are falling, trade proportions are rising, and regional trading patterns are becoming less extreme.” Ibid., 324. The time periods he utilizes and the commensurate degrees of openness and closure are: 1820–1879—increasing openness; 1879–1900—modest closure; 1900–1913—greater openness; 1918–1939—closure; 1945–1970—great openness.

³⁹ Gilpin (fn. 37), 58. Because a variety of other factors are not held constant in this exploratory analysis, this result can be regarded only as suggestive and tentative.

⁴⁰ Siverson, Randolf M. and Sullivan, Michael P., “The Distribution of Power and the Onset of War,” Journal of Conflict Resolution 27 (September 1983), 473–94CrossRefGoogle Scholar, at 474. Siverson and Sullivan present a good discussion of power preponderance and balance-of-power theory. For another thoughtful treatment of these types of theories, see Jack S. Levy, “Theories of war. For example, while both Henry Kissinger and Inis Claude argue that “the relatively equal distribution of power among the major actors in the international system brings about an equilibrium in which war is relatively unlikely,” Kenneth Waltz's brand of balance-of-power theory makes no explicit argument concerning the distribution of power and the probability of war. Siverson and Sullivan, 474; also see Kissinger, Henry, The White House Years (Boston: Little, Brown, 1979)Google Scholar; The White House Years (Boston: Little, Brown, 1979)Google Scholar; Claude, Inis L., Power and International Relations (New York: Random House, 1962)Google Scholar; Power and International Relations (New York: Random House, 1962)Google Scholar; and Waltz, Kenneth, Theory of International Politics (Reading, MA: Addison-Wesley, 1979)Google Scholar; Theory of International Politics (Reading, MA: Addison-Wesley, 1979)Google Scholar.

For leading examples of power-preponderance and power-transition theories, see Gilpin, Robert, War and Change in World Politics (New York: Cambridge University Press, 1981)CrossRefGoogle Scholar; War and Change in World Politics (New York: Cambridge University Press, 1981)Google Scholar; Modelski, George, “The Long Cycle of Global Politics and the Nation-State,” Comparative Studies in Society and History 20 (April 1978), 214–38CrossRefGoogle Scholar; Thompson, William, ed., Contending Approaches to World System Analysis (Beverly Hills, CA: Sage Publications, 1983)Google Scholar; Contending Approaches to World System Analysis (Beverly Hills, CA: Sage Publications, 1983)Google Scholar; Organski, A.F.K., World Politics (New York: Alfred A. Knopf, 1958)Google Scholar; World Politics (New York: Alfred A. Knopf, 1958)Google Scholar; Organski, A.F.K. and Kugler, Jacek, The War Ledger (Chicago: University of Chicago Press, 1980)Google Scholar; The War Ledger (Chicago: University of Chicago Press, 1980)Google Scholar; Doran, Charles F. and Parsons, Wes, “War and the Cycle of Relative Power,” American Political Science Review 74 (December 1980), 947–65CrossRefGoogle Scholar; and Väyrynen (fn. 34).

⁴¹ Gilpin (fns. 37 and 40); Modelski (fn. 40); Wallerstein, Immanuel, “The Three Instances of Hegemony in the History of the Capitalist World-Economy,” International journal of Comparative Sociology 24 (No. 1–2, 1983), 100–103CrossRefGoogle Scholar.

Gilpin's periods of hegemony are 1815–1914 (Great Britain) and 1945–1980 (United States). He does not specify exactly when or whether U.S. hegemony has ended; however, he asserts that “by the 1980s, American hegemonic leadership… had greatly eroded” (fn. 37, p. 345). For this reason, and because no data set extends beyond that year, 1980 is used as the final year of American hegemony. Modelski points out that he is interested in periods of “world leadership” rather than of hegemony. See Modelski, George, “Long Cycles, Kondratieffs, and Alternating Innovations: Implications for U.S. Foreign Policy,” in Kegley, Charles W. and McGowan, Patrick, eds., The Political Economy of Foreign Policy Behavior (Beverly Hills, CA: Sage Publications, 1981)Google Scholar; The Political Economy of Foreign Policy Behavior (Beverly Hills, CA: Sage Publications, 1981), 64Google Scholar. In such eras, power is less highly concentrated than under hegemony. Modelski's periods are 1494–1580 (Portugal); 1609–1688 (United Provinces of the Netherlands); 1713–1802 (Great Britain); 1815–1937 (Great Britain); and 1945–1980 (United States). The beginning of each cycle is given by the year Modelski provides for the “legitimizing settlement.” When more than one year is provided, the most recent is employed. The end of each cycle is marked by “landmarks of descent.” For each cycle, the final year of the most recent landmark is utilized. See Modelski (fn. 40), 225. The war data employed do not extend beyond 1980; moreover, no landmarks of descent are provided for the United States. Hence, 1980 is used as the final year of American leadership.

Wallerstein's periods are: 1625–1672 (United Provinces of the Netherlands); 1815–1873 (Great Britain); and 1945–1967 (United States). Any data prior to 1600 were excluded for Wallerstein's periods because this is when he dates the start of the modern system and it would be inappropriate to compare wars in different systems. Levy has also designated three periods of hegemony: 1556–1588, 1659–1713, and 1797–1815. See Levy, Jack S., “The Polarity of the System and International Stability: An Empirical Analysis,” in Sabrosky, Alan Ned, ed., Polarity and War: The Changing Structure of International Conflict (Boulder, CO: West-view Press, 1985)Google Scholar; Polarity and War: The Changing Structure of International Conflict (Boulder, CO: West-view Press, 1985), 41–66Google Scholar. However, because Wright's data set was the only one to include wars that began prior to 1815, Levy's eras of hegemony were not included here (although they are included in the analysis of wars between and involving major powers).

⁴² If, in fact, a preponderance of power increases the probability of war, this could explain why the results based on Modelski's classifications are weaker than those based on the others. Modelski is referring to leadership, not hegemony (see fn. 41). Leadership is clearly a weaker form of power disparity than hegemony. Thus, the relationship might be expected to be weaker when his classification is used than when the others are used.

⁴³ Various datings of hegemony also elicit different results. When Modelski's periods are examined and only international wars are employed, the lack of leadership seems to be associated with a relatively high incidence of war; Gilpin's and Wallerstein's periods produce very different results.

⁴⁴ Power transition theorists generally conclude that most wars, and the most serious wars, tend to be fought during periods in which the system is shifting from a non-hegemonic to a hegemonic or from a hegemonic to a non-hegemonic distribution of power.

⁴⁵ Singer and Small (fn. 1), 70, provide an initial compilation of thirty major-power wars. Using their coding scheme, I updated this list with the additional data they provide in Resort to Arms (fn. 1), thereby adding two other wars to their original data: the Russo-Afghan War (1979) and the Sino-Vietnamese War (1979).

⁴⁶ The incidence of wars involving major states for Singer and Small's list, and between Great Powers in Levy's, was too small to conduct a Chi-square test for goodness-of-fit: if the expected number in each class exceeds 5, no degrees of freedom existed. The conclusions, then, are based on the comparison of histograms in Figure 11 showing the theoretical and observed frequency distributions. For Levy's data involving major powers, a Chi-square test was conducted (X ² = 1.69.10 < p <.20). Clearly, we cannot reject the null hypothesis that the data conform to the Poisson distribution.

⁴⁷ Levy also found a downward trend in the onset of wars between and involving major powers. See Levy (fn. 1), 112–49.

⁴⁸ Goldstein (fn. 31) makes the same observation, based on Levy's data. However, Singer and Small's data support the thesis that more wars tend to begin in upswings than in downswings of the Kondratieff cycle. (See Table 6.) Although I am not implying a causal relationship between Kondratieff waves, or international trade, and war, the results do seem to indicate that certain circumstances in the international economy are more conducive to the outbreak of warfare than are others.

⁴⁹ There do seem to be important differences across classifications of hegemony and non-hegemony. Gilpin's classification consistently elicits a higher mean number during periods of non-hegemony, whereas Wallerstein's and Levy's classifications provide consistent results that point in the opposite direction.

⁵⁰ These results are interesting in light of earlier findings by Singer, Bremer, and Stuckey that, while power preponderance seems to have inhibited wars involving major powers between 1816 and 1965, the “goodness-of-fit was not very impressive. “Singer, J. David, Bremer, Stuart, and Stuckey, John, “Capability Distribution, Uncertainty, and Major Power Wars, 1820–1965,” in Russett, Bruce M., ed., Peace, War, and Numbers (Beverly Hills, CA: Sage Publications, 1972)Google Scholar; Peace, War, and Numbers (Beverly Hills, CA: Sage Publications, 1972), 46Google Scholar. This would seem to lend support for their conclusion that no single theory concerning the distribution of power explains the outbreak of warfare very well over long periods of time. These authors therefore argue that, for a more fruitful approach, the data should be split between the 19th and 20th centuries. Similarly, Bruce Bueno de Mesquita has found that “no particular distribution of power has exclusive claim as a predictor of peace or war either in theory or in the empirical record of the period 1816–1965. See “Risk, Power Distributions, and the Likelihood of War,” International Studies Quarterly 25 (December 1981), 541CrossRefGoogle Scholar; emphasis in original.