¹ For statements of classical “balance of power” theory, see Mowat, R. W., The European States System (London: Oxford University Press, 1929)Google Scholar; Friedrich, Carl J., Foreign Policy in the Making (New York: Norton, 1938)Google Scholar; Morgenthau, Hans J., Politics Among Nations (4th ed.; New York: Knopf, 1967), Part IVGoogle Scholar; Schuman, Frederick L., International Politics (6th ed.; New York: McGraw-Hill, 1958), pp. 70–72, 275–78, 577–79, 591–92Google Scholar; Wight, Martin, Power Politics (London: Royal Institute of International Affairs, 1946)Google Scholar. See also Haas, Ernst B., “The Balance of Power: Prescription, Concept or Propaganda?” World Politics, V (July, 1953), 442–77CrossRefGoogle Scholar.

² Kaplan, Morton A., System and Process in International Politics (New York: Wiley, 1957), Ch. II, V, VIGoogle Scholar; Kaplan, , “Intervention in Internal War: Some Systemic Sources,” International Aspects of Civil Strife, ed. Rosenau, James N. (Princeton: Princeton University Press, 1964), pp. 92–121Google Scholar. For other codifications, see Claude, Inis L. Jr., Power and International Relations (New York: Knopf, 1962), pp. 11–93Google Scholar; Gulick, Edward V., Europe's Classical Balance of Power (Ithaca: Cornell University Press, 1955)Google Scholar; Liska, George, International Equilibrium (Cambridge: Harvard University Press, 1957), pp. 187–202CrossRefGoogle Scholar; Wolfers, Arnold, Discord and Collaboration (Baltimore: Johns Hopkins Press, 1962), pp. 117–32Google Scholar.

³ Waltz, Kenneth N., “Stability of the Bipolar World,” Daedelus, XCIII (Summer, 1964), 881–909Google Scholar.

⁴ Among the advocates of multipolarity we may count Masters, Roger D., “A Multi-Bloc Model of the International System,” this Review, LV (December, 1961), 780–98Google Scholar. Bipolarity is favored by Aron, Raymond, “The Quest for a Philosophy of Foreign Affairs,” Contemporary Theory in Inlernational Relations, ed. Hoffmann, Stanley (Englewood Cliffs: Prentice-Hall, 1960), pp. 79–91Google Scholar; Etzioni, Amitai, Political Unification (New York: Holt, Rinehart, Winston, 1965), pp. 69–70Google Scholar. See, however, Griffith, William E., “Eppuor Se Muove,” Daedelus, XCIII (Summer, 1964), 916–19Google Scholar.

⁵ Deutsch, Karl W. and Singer, J. David, “Multipolar Power Systems and International Stability,” World Politics, XVI (April, 1964), 390–406CrossRefGoogle Scholar.

⁶ Rosecrance, Richard N., “Bipolarity, Multipolarity, and the Future,” Journal of Conflict Resolution, X (September, 1966), 314–27CrossRefGoogle Scholar.

⁷ Rosecrance, Richard N., Action and Reaction in World Politics (Boston: Little, Brown, 1963)Google Scholar. For some critiques, see Liska, George, “Continuity and Change in International Systems,” World Politics, XVI (October, 1963), 118–36CrossRefGoogle Scholar; Rosenau, James N., “The Functioning of International Systems,” Background, VII (November, 1963), 111–18CrossRefGoogle Scholar; Zinnes, Dina A., “The Requisites for International Stability,” Journal of Conflict Resolution, VIII (September, 1964), 301–305CrossRefGoogle Scholar; Singer, J. David, “The Global System and Its Sub-Systems: A Developmental View,” Linkage Politics, ed. Rosenau, James N. (New York: Free Press, 1969), pp. 21–43Google Scholar.

⁸ Singer, J. David and Small, Melvin, “Alliance Aggregation and the Onset of War, 1815–1945,” Quantitative International Politics, ed. Singer, (New York: Free Press, 1968), pp. 247–86Google Scholar.

⁹ “Stability” is most customarily defined as behavioral change over time, such as in Haas, Michael, “Types of Asymmetry Within Social and Political Systems,” General Systems, XII (1967), 69–79Google Scholar. Rosecrance's definition deals with the extent of regulatory potency in coping with instability.

¹⁰ A common semantic trap is to say that a “system” exists only when it reaches some sort of threshold level in frequency of social interactions. Certainly it is more consistent with general systems analysis to define a system as any set of parts that are related in some way; and a classification of all types of relations would clearly be incomplete without the category “interacting,” for which one could assemble data to differentiate systems interacting at high and low levels. Entities, in short, are to be described with reference to conceptual variables, instead of being defined mystically in terms of thresholds. Such an approach is consistent with the “constructivist” systems approach advocated by Easton, David, A Framework for Political Analysis (Englewood Cliffs: Prentice-Hall, 1965), pp. 30–34Google Scholar.

¹¹ Rosenau, op. cit.

¹² Lasswell, Harold D. and Kaplan, Abraham, Power and Society (New Haven: Yale University Press, 1950), pp. 78–80, 252–54Google Scholar.

¹³ McNeill, William, A World History (New York: Oxford University Press, 1967)Google Scholar.

¹⁴ Brecher, Michael, “International Relations and Asian Studies: The Subordinate State System of Southern Asia,” World Politics, XV (January, 1963), 221–35Google Scholar. For a more complete justification for the criteria, which are three fewer than Brecher's original formulation, see Haas, Michael, International Conflict (Indianapolis: Bobbs-Merrill, forthcoming), Ch. IXGoogle Scholar. The concept of subordinate system, which seems to have meaning only when applied to a set of actors that are satellites of some superordinate state, thus is not relevant here.

¹⁵ Singer and Small, op. cit., use two criteria—diplomatic recognition by France or England, and a population of 500,000 or more. These criteria would of course exclude the Vietcong and other actors which, though subnational, are clearly militarily independent and internationally active due to their confrontation with countries outside of the state of which they are supposedly a part. See their “The Composition and Status Ordering of the International System,” World Politics, XVIII (January, 1966), 236–82Google Scholar; Russett, Bruce M., Singer, Small, “National Political Units in the 20th Century: A Standardized List,” this Review, LXII (September, 1968), 932–51Google Scholar.

¹⁶ The “stakes of conflict” criterion is proposed by Hoffmann, Stanley, “International Systems and International Law,” World Politics, XIV (October, 1961), 205–37CrossRefGoogle Scholar; cf. Rothstein, Robert L., “Power, Security and the International System,” paper presented to the American Political Science Association Annual Convention, Chicago, September, 1967Google Scholar; Hoffmann, , The State of War (New York: Praeger, 1965)Google Scholar.

¹⁷ Kaplan, op. cit. For a clarificatory essay, see Hanrieder, Wolfram F., “The International System: Bipolar or Multibloc?” Journal of Conflict Resolution, IX (September, 1965), 299–308CrossRefGoogle Scholar.

¹⁸ Denton, Frank, “Some Regularities in International Conflict, 1820–1949,” Background, IX (February, 1966), 283–96CrossRefGoogle Scholar. Denton analyzes data on wars collected by Richardson, Lewis F., Statistics of Deadly Quarrels (Chicago: Quadrangle, 1960)Google Scholar. The most exact validation procedure for subsystems defined in terms of poles and looseness would consist of an R-analysis of the number of poles recorded for each year in the years to be studied and a measure of the extent of looseness (or failure to pull all members of a system into one or more of the contending poles). Ordinal data to construct such indicators is not easily at hand, and since we have already assigned 0 and 1 codings implicitly in the discussion to follow, an R-analysis of nominal scale codings would doubtless be a trivial exercise.

¹⁹ I wish to express my gratitude to Professors Charles Hunter, Werner Levi, and Norman Meller for offering assistance in my analysis of the Asian and Hawaiian materials. The scarcity of scholars able to assess my extraction of subsystems in Asia and Hawaii precluded a Delphi procedure such as the one apparently undertaken by Rosecrance. See Rosecrance, Action and Reaction in World Politics, op. cit., p. x; Helmer, Olaf, Convergence of Expert Consensus Through Feedback (Santa Monica: Rand, 1664)Google Scholar. I have altered the dates of some of Rosecrance's subsystems so as to eliminate overlapping years, thereby enabling a smoother data collection procedure.

²⁰ M. Haas, loc. cit. The European eras are most succinctly described in Mowat, op. cit.; Hill, David Jayne, A History of Diplomacy in the International Development of Europe (New York: Longmans, Green, 1914)Google Scholar; and Rosecrance, Action and Reaction in World Politics, op. cit. For Asia, see Vinacke, Harold M., A History of the Far East in Modern Times (6th ed.; New York: Appleton-Century-Crofts, 1959)Google Scholar; MacNair, Harley P. and Lach, Donald F., Modern Far Eastern International Relations (2nd ed.; New York: Van Nostrand, 1955)Google Scholar. The major sources on Hawaii are Fornander, Abraham, An Account of the Polynesian Race (vol. II; London: Trubner, 1880)Google Scholar; Kuykendall, Ralph S. and Day, A. Grove, Hawaii (rev. ed.; Englewood Cliffs: Prentice-Hall, 1961)Google Scholar; Kuykendall, , The Hawaiian Kingdom, 1854–1874 (Honolulu: University of Hawaii Press, 1953)Google Scholar; Stevens, Sylvester K., American Expansion in Hawaii, 1848–1898 (Harrisburg: Achives Publishing, 1945)Google Scholar. A more monographic presentation would be preferable, so the reader should consult sources cited in these works for more complete accounts.

²¹ Singer and Small, “Alliance Aggregation and the Onset of War, 1815–1945,” loc. cit. I have supplemented these data with a compilation of alliances between members of the five Hawaiian subsystems based on Fornander, loc cit. Definitions of each variable appear in the Appendix to this paper. Data are available upon request from the author.

²² Since none of the variables depart significantly from normal curve distributions, though they tend to be rectangular in view of the small sample size, product-moment correlations were computed between the 33 variables. A principle axis factor analysis, with 1.0, was run, and there was a negative eigenvalue on the 14th cycle. An orthogonal (varimax) rotation, after determining the number of factors from the eigenvalue 1.0 criterion, approximated simple structure, so a quartimin rotation was performed, using an oblimin program developed by John Carroll; gamma was set at 0.0, and the solution ran 30 cycles, 13 500 iterations. A biquartimin rotation was tested but, in conformity with the observation that varimax was very close to simple structure, factor loadings were so greatly inflated in value as to be meaningless.

²³ Factor number assignments coming from the unrotated solution often do not correspond with oblique solutions; the unrotated factors, which are brought into a clearer form through an orthogonal rotation, denote a succession of factors starting with the most important (in terms of variance explained) and decreasing to the least important. Here we follow the numbering of the quartimin factors, for the sake of clarity in reading the results.

²⁴ Factor VIII seems to indicate Imperial Expansion; IX, Imperial Decline.

²⁵ Richardson, op. cit., pp. 33–111. The supplementary sources are Fornander, loc. cit., and data supplied by Mr. Richard Cady, Bendix Systems Division, Ann Arbor, from a study of low-intensity warfare sponsored by the Office of Naval Research, Contract NC0014–66–CO262.

²⁶ Wright, Quincy, A Study of War (2nd ed.; Chicago: University of Chicago Press, 1965), pp. 644–49Google Scholar. In view of his more formal criteria it would not appear consistent to add Hawaii data to his list; for the same reason I have deducted subnational members from the total number of members in norming variable 54, as well as 17 and 19. Two other sources, Singer and Small, and Sorokin, employ restrictive criteria that made their lists less useful for the particular purposes of this study: Singer and Small do not include interventions, and their data pertain only to 1815–1945; Sorokin assembles data only for about 10 countries, though over a very long time period. Singer and Small, “Alliance Aggregation and the Onset of War, 1815–1945,” loc. cit.; Sorokin, Pitirim A., Fluctuations of Social Relationships, War and Revolution (New York: American Book Company, 1937), pp. 547–77Google Scholar.

²⁷ A principal axis factor analysis was performed on the 19 × 19 correlation matrix with unities in the diagonal. Six factors emerged with eigenvalues over 1.0, and negative eigenvalues were encountered on the ninth cycle. An orthogonal (varimax) rotation was next run, and the subsequent biquartimin solution (30 cycles, 9000 iterations) was virtually identical in higher loadings with the orthogonal solution though much cleaner with regard to intermediate loadings. Accordingly, only the biquartimin P matrix is presented in Table 3. The only high interfactor correlation is −.60, between factors I and V.

²⁸ The Pearsonian 17 × 17 matrix input to a principal axis factor analysis with 1.0 in the diagonal. Five factors emerged with eigenvalues over 1.0, and a negative eigenvalue terminated the run on the eleventh cycle. An orthogonal (varimax) rotation was performed and a subsequent biquartimin rotation took 30 cycles, 16469 iterations. The only high interfactor correlation is −.70, between factors III and V.

²⁹ Guttman, Louis, “A General Nonmetric Technique for finding the Smallest Coordinate Space for a Configuration of Points,” Psychometrika, XXXIII (December, 1968), 469–506CrossRefGoogle Scholar; Ward, Joe H. Jr., “Hierarchical Grouping to Optimize on Objective Function,” American Statistical Association Journal, LVIII (March 1963), 236–44CrossRefGoogle Scholar. The specific code names are SSA-I for the former, and Cluster IV for the latter.

³⁰ The 52 × 52 correlation matrix in the diagonal. Twelve factors were extracted with eigenvalues greater than 1.0, and negative eigenvalues appeared on the fourteenth cycle. An orthogonal (varimax) rotation was performed but so many communalities exceeded 1.0 (due to missing data) that it was impossible to obtain a meaningful oblique solution.

³¹ The storage limitation for smallest space analysis on the IBM 7040 at the University of Hawaii Computing Center was 50 variables, so the stratification data (33 variables) were reduced by two variables in the analysis with Richardson's data (19 variables). The excluded variables were number 1 (number of poles), which has emerged on the same factor with multipolarity in every run attempted with factor analysis, and variable 27, which has similarly been so related with another variable (number 26) as to be superfluous in a larger analysis. Isobars in the SSA-I figures are drawn around variables on the basis of loadings ±.50 in the factor analyses reported in Tables 2–4. Lower case Roman numerals refer to the stratification factors; upper case, to Richardson's dimensions in Figure 1, and to Wright's dimension in Figure 2. Labels are not attached to each variable number, since the names given in Tables 2–3 are so lengthy that they would clutter the plot unesthetically.

³² A factors analysis of the 33 stratification and 17 Wright variables once again produced results that were unsatisfactory in technical respects—inflated communalities, failure of an oblique solution to improve simple structure from an othogonal solution. A principal axis factor analysis was first attempted with 1.0 in the diagonal, nine factors emerging with eigenvalues exceeding 1.0 and a negative root was encountered on the tenth cycle. The varimax findings, however, were somewhat sharper: (1) Multipolarity and Size collapse alone with War Incidence on the first factor; (2) Size and Multilaterality, on factor II; (3) War Incidence and Differentiation load high on factor III, but are inversely related. None of the remaining factors recombine any of the dimensions discovered in the preliminary analysis.

³³ Smallest space analysis was precluded because of the 50-variable limit. The data input to the cluster analysis was the 68 × 68 Pearsonian correlation matrix.

³⁴ The four main clusters converge as follows: the unipolar and bipolar clusters merge at −92.5356; the tripolar and multipolar clusters collapse at −102.5750; and the entire set of 68 variables come together at a similarity coefficient of −119.9040.

³⁵ A principal axis factor analysis on the 68 × 68 Pearsonian correlation matrix extracted seven factors, with a negative root encountered on the eighth cycle. The orthogonal (varimax) loadings were input to a quartimin oblique rotation, which ran 30 cycles, 28500 interations, a biquartimin solution having turned up an unacceptable abundance of inflated factor loadings. The findings are similar to those derived from the cluster analysis: (1) Multipolarity and Size collapsed along with War Incidence on factor I; (2) Procrusteanness and subsystem Size are related to Extrasystem Wars; (3) Size is linked to Multilateral Wars; (4) Alliance Saturation and Extra-Era War dimensions are found together; (5) Alliance Saturation is related to Duration and Destabilization on two factors, one for Richardson and the other for Wright. The meaning of the seventh factor is not clear. These results are not presented here because they reinforce previous findings and, thus, would be redundant information; yet another reason, however, is that the polarity codings, our main interest herein, receive no significant loadings. Cluster analysis does not bury the relationships one seeks to discover and is therefore discussed in more detail.