¹ New York: Wiley Science Editions, 1964. First published in 1957. All quotations of Kaplan in this paper are from the 1964 paperback reprint unless otherwise noted.

² Kaplan, , System and Process, preface and pp. 27–29, 35–36 Google Scholar.

³ Representative discussions may be found in: Liska, George, Nations in Alliance: The Limits of Interdependence (Baltimore: The Johns Hopkins University Press, 1962)Google Scholar; Friedman, Julian, Bladen, Christopher and Rosen, Steven, eds., Alliance in International Politics (Boston: Allyn and Bacon, 1970)Google Scholar; Claude, Inis Jr., Power and International Relations (New York: Random House, 1962)Google Scholar; Haas, Ernst B., “The Balance of Power: Prescription, Concept, or Propaganda,” World Politics, 5 (07, 1953), 442–447 CrossRefGoogle Scholar and “The Balance of Power as a Guide to Policy Making,” Journal of Politics, 15 (08, 1953), 370–398 CrossRefGoogle Scholar; Kaplan, System and Process; and Seabury, Paul, ed., Balance of Power (San Francisco: Chandler, 1965)Google Scholar.

⁴ Kaplan, , System and Process, pp. 22–23 Google Scholar. These rules are: “1. Act to increase capabilities, but negotiate rather than fight. 2. Fight rather than pass up an opportunity to increase capabilities. 3, Stop fighting rather than eliminate an essential national actor. 4. Act to oppose any coalition or single actor which tends to assume a position of predominance with respect to the rest of the system. 5. Act to constrain actors who subscribe to supranational organizing principles. 6. Permit defeated or constrained essential actors to re-enter the system as acceptable role partners or act to bring some previously inessential actor within the essential actor classification. Treat all essential actors as acceptable role partners.”

⁵ Kaplan, , System and Process, pp. 22, 28–29 Google Scholar.

⁶ Liska, , Nations in Alliance, p. 12 Google Scholar.

⁷ Friedman, Julian, “Alliance in International Politics,” in Alliance in International Politics, ed. Friedman, J. et al., pp. 4–5 Google Scholar and Modelski, George, “The Study of Alliances: A Review,” Journal of Conflict Resolution, 7 (12, 1963), 769–776 CrossRefGoogle Scholar provide discussions of the salient characteristics of alliances.

⁸ Representative discussions are: Kaplan, , System and Process, pp. 35, 66, 115 Google Scholar; Morgenthau, Hans J., Politics Among Nations: The Struggle for Power and Peace, 3rd ed. (New York: Knopf, 1963), pp. 167–223 Google Scholar; and Friedman, , “Alliance in International Politics,” p. 23 Google Scholar.

⁹ Kaplan, , System and Process, p. 125 Google Scholar. See also Friedman, pp. 21–22 for the “functions” of alliances in international systems.

¹⁰ These aspects of the role of alliances as a tool of foreign policy are further discussed in: Dinerstein, Herbert, “The Transformation of Alliance Systems,” American Political Science Review, 59 (09 1965), 589–601 CrossRefGoogle Scholar. See also: Liska, , Nations in Alliance, p. 16 Google Scholar; Kaplan, , System and Process, p. 66 Google Scholar; Cross, J. G., “Some Theoretic Characteristics of Economic and Political Coalitions,” Journal of Conflict Resolution, 11 (06, 1967), 187 CrossRefGoogle Scholar; and Masters, Roger, “A Multibloc Model of the International System,” American Political Science Review, 55 (12, 1961), 788 CrossRefGoogle Scholar.

¹¹ This “model” is clearly prescriptive, and hypothetically it is an accurate description and prediction of alliance politics in any balance of power system. Like other rational models, it mixes description, explanation and possible prescription, a point well made by Davis, Otto in “Notes on Strategy and Methodology for a Scientific Political Science,” in Mathematical Applications in Political Science IV, ed. Bernd, Joseph K. (Charlottesville: The University Press of Virginia, 1969), pp. 22–38 Google Scholar.

¹² Friedman, , “Alliance in International Politics,” p. 23 Google Scholar.

¹³ Burns, Arthur Lee, “From Balance to Deterrence: A Theoretical Analysis,” World Politics, 9 (07, 1957), 495 CrossRefGoogle Scholar.

¹⁴ Kaplan, , System and Process, preface to the 1964 Wiley Science Edition Google Scholar.

¹⁵ Ibid.

¹⁶ Heuristic, of course, does not mean general; it means serving to discover. Professor Kaplan is not alone, however, in apparently equating the two terms.

¹⁷ Kaplan, , System and Process, 1964 prefaceGoogle Scholar.

¹⁸ Ibid., p. 24, and Kaplan, Morton A., “Some Problems in International Systems Research,” in International Political Communities: An Anthology (Garden City: Doubleday Anchor Books, 1966), p. 471 Google Scholar.

¹⁹ Kaplan, , System and Process, p. 24 Google Scholar.

²⁰ Ibid., pp. 66, 115–116.

²¹ Ibid., preface.

²² Lindley, D. V., Introduction to Probability and Statistics from a Bayesian Viewpoint, Part I, Probability (Cambridge: Cambridge University Press, 1965), p. 67 CrossRefGoogle Scholar.

²³ The metaphor, which comes in the middle of Kaplan's discussion of the operation of balance of power, is worth quoting in full. “Just as any particular molecule of gas in a gas tank may travel in any direction, depending upon accidental bumpings with other molecules, particular actions of national actors may depend upon chance or random conjunctions. Yet just as the general pattern of behavior of gas may represent its adjustment to pressure and temperature conditions within the tank, the set of actions of national actors may correspond to the essential rules of the system when the other variables take the appropriate specified values.

Thus, by shifting the focus of analysis from the particular event to the pattern of events, seemingly unique or accidental occurrences become part of a meaningful pattern of occurrences. In this way the historical loses its quality of uniqueness and is translated into the universal language of science” (System and Process, p. 25).

Professor Richard E. Hayes of C.A.C.I., Inc. disagrees with our reading of Kaplan's example, arguing in a personal communication that the metaphor refers to the limited predictability of social systems in general. Our disagreement illustrates the difficulties involved in deriving falsiflable hypotheses from verbal “theories” and “models” such as Kaplan's.

²⁴ An authoritative survey is given by Feller, William, An Introduction to Probability Theory and Its Applications, 3rd ed. (New York: Wiley, 1968)Google Scholar.

²⁵ Discussions of the Poisson distribution and the uniqueness of Poisson processes from a variety of perspectives are presented by: Raiflfa, Howard and Schlaifer, Robert, Applied Statistical Decision Theory (Cambridge, Mass.: MIT Press, 1961), pp. 275–276 Google Scholar; Kempthome, Oscar and Folks, Leroy, Probability, Statistics, and Data Analysis (Ames: The Iowa State University Press, 1971), pp. 199–200 Google Scholar; Coleman, James S., Introduction to Mathematical Sociology (Glencoe: The Free Press, 1964), pp. 288–289 Google Scholar; Lindley, , Introduction to Probability and Statistics, pp. 63–73 Google Scholar; Hayes, Richard E., “Identifying and Measuring Changes in the Frequency of Event Data,” International Studies Quarterly, 17 (12, 1973), 471–493 CrossRefGoogle Scholar.

²⁶ Lindley, , Introduction to Probability and Statistics, p. 68 Google Scholar.

²⁷ Kaplan, , System and Process, p. 35 Google Scholar.

²⁸ Schuessler, Karl, Analyzing Social Data: A Statistical Orientation (New York and Boston: Houghton Mifflin Co., 1971), p. 412 Google Scholar; Kempthorne, and Folks, , Probability, Statistics and Data Analysis, p. 91 Google Scholar.

²⁹ Yule, G. U. and Kendall, M. G., An Introduction to the Theory of Statistics, 14th rev. and enlarged ed. (New York: Hafner, 1950), p. 169 Google Scholar.

³⁰ Kaplan, , System and Process, preface and pp. 8, 35–36, 54–85 Google Scholar.

³¹ Ibid., p. 74.

³² Ibid., pp. 35, 125.

³³ Ibid., pp. 27–29, 74.

³⁴ Chi, Hsi-sheng, “The Chinese Warlord System as An International System,” pp. 405–425 Google Scholar and Franke, Winfried, “The Italian City-State System as an International System,” pp. 426–458 Google Scholar, both in New Approaches to International Relations, ed. Kaplan, Morton A. (New York: St. Martin's Press, 1968)Google Scholar.

³⁵ Healy, Brian and Stein, Arthur, “The Balance of Power in International History: Theory and Reality,” Journal of Conflict Resolution, 17 (03, 1973), 33–61 CrossRefGoogle Scholar.

³⁶ See Julian Friedman et al., eds., Alliance in International Politics, for a survey of this literature.

³⁷ Singer, J. David and Small, Melvin, “Formal Alliances, 1815–1939: A Quantitative Description,” Journal of Peace Research, 3/1 (01 1966), 1–32 CrossRefGoogle Scholar; “Alliance Aggregation and the Onset of War, 1815–1945,” in Quantitative International Politics: Insights and Evidence, ed. Singer, J. D. (New York: The Free Press, 1968), pp. 245–286 Google Scholar; “National Alliance Commitments and War Involvement, 1815–1945,” Peace Research Society (International) Papers, 5 (1966), 109–140 Google Scholar; and “Formal Alliances, 1816–1965: An Extension of the Basic Data,” Journal of Peace Research, No. 3, (1969), 257–282 Google Scholar.

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³⁹ de Mesquita, Bruce Bueno and Singer, J. D., “Alliances, Capabilities, and War: A Review and Synthesis,” in Political Science Annual, ed. Cotter, C. P. (Indianapolis: Bobbs-Merrill, 1973), IV, 237–280 Google Scholar and Wallace, Michael, “Alliance Polarization, Cross-Cutting, and International War, 1815–1964: A Measurement Procedure and Some Preliminary Evidence,” Journal of Conflict Resolution, 17 (12, 1973), 575–604 CrossRefGoogle Scholar.

⁴⁰ Richardson, Lewis Fry, “The Distribution of Wars in Time,” Journal of the Royal Statistical Society, 107 (1945), 242–250 CrossRefGoogle Scholar; Moyal, J. R., “The Distribution of Wars in Time,” Journal of the Royal Statistical Society, Series A, 112 (1949), 446–449 CrossRefGoogle Scholar.

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⁴² Singer, J. David and Small, Melvin, The Wages of War, 1816–1965: A Statistical Handbook (New York: John Wiley, 1972), pp. 205–206 Google Scholar.

⁴³ Midlarsky, Manus, “Mathematical Models of Instability and a Theory of Diffusion,” International Studies Quarterly, 14 (03, 1970), 60–84 CrossRefGoogle Scholar.

⁴⁴ Wilkenfeld, Jonathan, “Models for the Analysis of Foreign Conflict Behavior of States,” in Peace, War and Numbers, ed. Russett, B. M. (Beverly Hills: Sage Publications, 1972), pp. 275–298 Google Scholar and Zinnes, Dina A. and Wilkenfeld, Jonathan, “An Analysis of Foreign Conflict Behavior of Nations,” in Comparative Foreign Policy, ed. Hanrieder, W. F. (New York: David McKay, 1971), pp. 167–213 Google Scholar.

⁴⁵ Zinnes, Dina A., Zinnes, J. L. and McClure, R. D., “Hostility in Diplomatic Communication: A Study of the 1914 Crisis,” in International Crises, ed. Hermann, C. F. (New York: The Free Press, 1972), pp. 139–162 Google Scholar.

⁴⁶ Horvath, W. J. and Foster, C. C., “Stochastic Models of War Alliances,” Journal of Conflict Resolution, 7 (06, 1963), 110–116 CrossRefGoogle Scholar.

⁴⁷ Rood, Robert M., “Agreement in the International System,” (Ph.D. dissertations in Political Science, Syracuse University, 1973)Google Scholar; Brams, Steven J. and O'Leary, Michael, “An Axiomatic Model of Voting Bodies,” American Political Science Review, 64 (06, 1970), 449–470 CrossRefGoogle Scholar.

⁴⁸ Job, Brian, “Alliance Formation in the International System: The Application of the Poisson Model,” a paper presented at the Annual Meeting of the International Studies Association, Americana Hotel, New York (03 13–17, 1973)Google Scholar.

⁴⁹ Siverson, Randolph M. and Duncan, G. T., “Stochastic Models of International Alliance Initiation, 1815–1965,” Department of Political Science University of California, Davis, mimeo, n.d. [1973?], p. 12 Google Scholar.

⁵⁰ Raiffa, and Schlaifer, , Applied Statistical Decision Theory, p. 283 Google Scholar.

⁵¹ Ibid.

⁵² The best discussion of social scientific applications of the Poisson distribution is given in Coleman, J. S., Introduction to Mathematical Sociology, pp. 288–380 Google Scholar.

⁵³ Discussions of aspects of events data making are given in: Azar, Edward, “Analysis of International Events,” Peace Research Reviews, 4, No. 1 (1970)Google Scholar; Azar, Edward, Brody, R. A., and McClelland, C. A., International Event Interaction Analysis: Some Research Considerations, Sage Professional Paper in International Studies 02–001 (Beverly Hills and London: Sage Publications, 1972)Google Scholar; Hermann, C. F., “What is a Foreign Policy Event?” pp. 295–321 Google Scholar in Comparative Foreign Policy, ed. Hanreider; Burgess, P. M. and Lawton, R. W., Indicators of International Behavior: An Assessment of Events Data Research. Sage Professional Paper in International Studies 02–010 (Beverly Hills and London: Sage Publications, 1972)Google Scholar; and McGowan, P. J., “A Bayesian Approach to the Problem of Events Data Validity,” pp. 407–433 Google Scholar in Comparing Foreign Policies, ed. Rosenau, J. N. (New York: Halsted Press (a Sage Publications Book), 1974)Google Scholar.

⁵⁴ Brian Healy and Arthur Stein, “The Balance of Power in International History: Theory and Reality,” Goodman, Ronald, Hart, Jeff, and Rosecrance, Richard, “Testing International Relations Theory: Methods and Data in a Situational Analysis of International Politics,” Ithaca: Cornell University Situational Analysis Project Paper No. 2, mimeo, 01, 1970 Google Scholar; and Hart, Jeff, “Symmetry and Polarization in the European International System: 1870–1879,” Ithaca: Cornell University Situational Analysis Project Paper No. 3, mimeo, (1972)Google Scholar.

⁵⁵ As described in Rood, , “Agreement in the International System,” pp. 171–175 Google Scholar.

⁵⁶ Our sources were: Albrecht-Carrié, René, A Diplomatic History of Europe Since the Congress of Vienna (New York: Harper, 1958)Google Scholar; Gulick, E. V., Europe's Classical Balance of Power (New York: W. W. Norton, 1955)Google Scholar; Kissinger, H. A., A World Restored: Metternich, Castlereagh and the Problems of Peace, 1812–22 (Boston: Houghton Mifflin, 1957)Google Scholar; Langer, W. L., European Alliances and Alignments, 1871–1890, 2nd ed. (New York: Random House-Vintage Books, 1964)Google Scholar; Lobanov-Rostovsky, Andrei, Russia and Europe 1825–1878 (Ann Arbor: George Whar Publishing, 1954)Google Scholar; Mowat, R. B., The European States System: A Study of International Relations, 2nd ed. (London: Oxford University Press, 1929)Google Scholar; Seaman, L. C. B., From Vienna to Versailles (New York: Harper, 1963)Google Scholar; Seton-Watson, R. W., Britain in Europe, 1789–1914 (New York: Howard Fertig, 1968)Google Scholar; and Taylor, A. J. P., The Struggle for Mastery in Europe 1848–1918 (Oxford: The Clarendon Press, 1954)Google Scholar.

⁵⁷ Taylor, , The Struggle for Mastery in Europe, pp. 2–3, 34–35 Google Scholar.

⁵⁸ As described in Singer and Small, “Formal Alliances, 1815–1939,” and “Formal Alliances, 1816–1965.”

⁵⁹ Rood, , “Agreement in the International System,” pp. 183–201. This dissertation is available from University Microfilms in Ann Arbor, Michigan Google Scholar.

⁶⁰ Ibid., pp. 171–202.

⁶¹ Singer, and Small, , “Formal Alliances, 1815–1939,” pp. 24–27 Google Scholar.

⁶² Rood, , “Agreement in the International System,” pp. 64–67 Google Scholar.

⁶³ Rosecrance, R. N., Action and Reaction in World Politics (Boston: Little, Brown, 1963), pp. 239–256 Google Scholar.

⁶⁴ Supporting this argument are: Gulick, , Europe's Classical Balance of Power, p. 4 Google Scholar; Morgenthau, , Politics Among Nations, p. 201 Google Scholar; Singer, J. David and Small, Melvin, “National Alliance Commitments and War Involvement, 1815–1945,” in International Politics and Foreign Policy, ed. Rosenau, J. N., 2nd ed. (New York: The Free Press, 1969), p. 515 Google Scholar.

⁶⁵ Singer, and Small, , “National Alliance Commitments …,” p. 515 in the Rosenau readerGoogle Scholar.

⁶⁶ Albrecht-Carrié, , A Diplomatic History of Europe, pp. 9–17 Google Scholar; Taylor, , The Struggle for Mastery in Europe, p. 54 Google Scholar; Seton-Watson, , Britain in Europe, p. 312 Google Scholar; and Dehio, Ludwig, The Precarious Balance: Four Centuries of the European Power Struggle (New York: Random House-Vintage Books, 1962)Google Scholar, passim.

⁶⁷ Feller, , An Introduction to Probability Theory, p. 156 Google Scholar, who argues that the three principal distributions are the binomial, the normal, and the Poisson, a point agreed to by Yule, and Kendall, , An Introduction to the Theory of Statistics, p. 169 Google Scholar.

⁶⁸ Feller, pp. 153–164; Lindley, , An Introduction to Probability and Statistics from a Bayesian Viewpoint, pp. 63–74 Google Scholar; Mendenhal, William and Scheaffer, Richard L., Mathmatical Statistics with Applications (North Scituate, Mass.: Duxbury Press, 1973), pp. 81–85 Google Scholar; Raiffa, and Schlaifer, , Applied Statistical Decision Theory, pp. 221–222, 275–289 Google Scholar; and Yule and Kendall, pp. 189–194.

⁶⁹ Haight, F. A., Handbook of the Poisson Distribution (New York: Wiley, 1967)Google Scholar; Kitagawa, T., Tables of Poisson Distribution (Tokyo: Baifukan, 1952)Google Scholar.

⁷⁰ Coleman, , An Introduction to Mathematical Sociology, pp. 288–311 Google Scholar.

⁷¹ Lindley, , An Introduction to Probability and Statistics, pp. 63–73 Google Scholar.

⁷² We give only the theorems presented by Lindley relevant to this paper.

⁷³ Pearson, E. S. and Hartley, H. O., Biometrika Tables for Statisticians, Volume I, 3rd ed. (Cambridge: Cambridge University Press, 1966), pp. 11–12 Google Scholar; Yule and Kendall, pp. 469–477.

⁷⁴ That is, only when X ² is large, so that for a given degree of freedom its probability is less than .10 or .05, is the null hypothesis rejected and the inference made that the observed distribution was not generated by a Poisson process. This is not a very conservative procedure. It unfortunately leaves open the possibility of Type II error, i.e., the inference that the null hypothesis prevails when in fact the alternate hypothesis is correct.

⁷⁵ Kempthorne, and Folks, , Probability, Statistics, and Data Analysis, p. 92 Google Scholar.

⁷⁶ Hayes, Richard E., “Identifying and Measuring changes in the Frequency of Event Data,” International Studies Quarterly, 17 (12, 1973), 471–493 CrossRefGoogle Scholar.

⁷⁷ Coleman, , An Introduction to Mathematical Sociology, pp. 291, 299 Google Scholar.

⁷⁸ Kaplan, , System and Process, 1964 prefaceGoogle Scholar.

⁷⁹ Lindley, , An Introduction to Probability and Statistics, p. 70 Google Scholar.

⁸⁰ Kitagawa, , Tables of Poisson Distribution, p. 65 Google Scholar.

⁸¹ Rosecrance, , Action and Reaction in World Politics, pp. 232–266 Google Scholar.

⁸² Denton, F. H., “Some Regularities in International Conflict, 1820–1949,” Background, 9 (02, 1966), 283–296 CrossRefGoogle Scholar. This journal is now the International Studies Quarterly.

⁸³ This research is under way. In a recent paper we correlated our alliance flexibility scores with the Singer and Small interstate war data for the same period of time and for our five actors only. We found strong and statistically significant evidence for the hypotheses that alliance formation (hence balance of power system flexibility) is negatively associated with the occurrence of war and war magnitude, severity and intensity ( Rood, R. M. and McGowan, P. J., “Flexibility in Balance of Power Alliance Systems and International War,” a paper delivered at the Third Annual Conference of the Southern Section of the Peace Science Society [International], Durham: Duke University, 04 4–5, 1974)Google Scholar. Our findings represent an independent replication of the well-known results of Singer and Small that alliance aggregation in the nineteenth century was negatively related to warfare; see Singer and Small, “National Alliance Commitments and War Involvement, 1815–1945,” and “Alliance Aggregation and the Onset of War, 1815–1945.”

⁸⁴ Richardson, , Statistics of Deadly Quarrels, pp. 128–142 Google Scholar; Singer, and Small, , The Wages of War, pp. 205–206 Google Scholar.