¹ “International Theory: The Case for a Classical Approach,” World Politics, XVIII (April 1966), 372Google Scholar.

² Rapoport, , Fights, Games, and Debates (Ann Arbor 1960), 45–46Google Scholar. Cf. Richardson, Generalized Foreign Policy, Monograph Supplement No. 23, British Journal of Psychology (June 1939)Google Scholar. For other contributions to the discussion of similar problems, see Boulding, Kenneth, Conflict and Defense: A General Theory (New York 1962)Google Scholar; Olson, Mancur Jr., and Zeckhauser, Richard, “An Economic Theory of Alliances,” Review of Economics and Statistics, XLVIII (August 1966), 266–79CrossRefGoogle Scholar; and Burns, Arthur Lee, “A Graphical Approach to Some Problems of the Arms Race,” Journal of Conflict Resolution, iii (December 1959), 326–42CrossRefGoogle Scholar.

³ Pp. 368–69. On the limitations of game theory in political science, see Burns, Arthur Lee, “Prospects for a General Theory of International Relations,” in Knorr, Klaus and Verba, Sidney, eds., The International System (Princeton 1961), 25–46Google Scholar; and Coddington, Alan, “Game Theory, Bargaining Theory, and Strategic Reasoning,” Journal of Peace Research, IV, No. 1 (1967), 39CrossRefGoogle Scholar.

⁴ Lipset, Seymour Martin treats the question in his book Political Man (New York 1960), chap. 2Google Scholar, “Economic Development and Democracy.” Lipset refers explicitly to Aristotle. Cf. also Deutsch, Karl W., “Basic Trends and Patterns in Politics,” American Political Science Review, LIV (March 1960), 34–57CrossRefGoogle Scholar; and Almond, Gabriel A. and Coleman, James S., eds., The Politics of the Developing Areas (Princeton 1960)Google Scholar, Conclusion and Statistical Appendix by James S. Coleman, 532ft. For the connection between political stability and the rate of economic development, see Olson, Mancur Jr., “Rapid Growth as a Destabilizing Force,” Journal of Economic History, XXIII (December 1963), 529–52CrossRefGoogle Scholar. Olson points out that economic change may be a factor sometimes favoring and sometimes endangering political stability.

⁵ Division and Cohesion in Democracy: A Study of Norway (Princeton 1966)Google Scholar, Appendix B, “A Theory of Stable Democracy,” 275.

⁶ It is not inconceivable that the agency in question may commit mistakes, buying or selling at the wrong moment, so that the instability of the market will be aggravated instead of decreased, in which case the agency will be an “unbalancer.” This too can be quantitatively ascertained.

⁷ Gulick, Edward Vose, Europe's Classical Balance of Power (New York 1955), 27Google Scholar. For a social scientist's point of view, see Coleman, James S., Introduction to Mathematical Sociology (New York 1964), 49–50Google Scholar.

⁸ How to Predict Elections (New York 1948), 54–55Google Scholar.

⁹ See my remarks in a letter to the editor of Public Opinion Quarterly, XIV (Fall 1950), 612Google Scholar, on the subject of an article by Tibbitts, Clark, “Majority Votes and the Business Cycle,” American Journal of Sociology, XXXVI (January 1931), 596–606CrossRefGoogle Scholar. Unlike Bean, Tibbitts concentrated on one region, the Northeast. His study has never been followed up.

¹⁰ See Siegfried, André, Géographic électorate de l'Ardèche (Paris 1949), 102Google Scholar. Similar high and low tides of clericalism were visible in northwestern France. But the fluctuations, the high and low tides, were not very marked, and fundamentally the situation remained stable, as in the Ardèche—stability being defined by Siegfried in quantitative terms: “. . . Les forces numeriques de la Droite . . . se maintiennent, avec une étonnante stabilité, autour de 27 p. 100 des inscrits” (Tableau politique de la France de l'Ouest sous la 3e République [Paris 1913], 461Google Scholar).

¹¹ References to the cobweb model can be found in a number of works on economics, such as Beach, E. F., Economic Models (New York 1957), 96Google Scholar; Lange, O., Introduction to Econometrics (New York 1963), 175Google Scholar; and Hood, William C. and Koopmans, Tjalling C., eds., Studies in Econometric Method (New York 1953), 18Google Scholar. For an application to a concrete case, see Suits, Daniel B., “An Econometric Model of the Watermelon Market,” Journal of Farm Economics, XXXVII (May 1955), 244Google Scholar.

¹² Anne to Lord Treasurer Godolphin, quoted from Trevelyan, G. M., England Under Queen Anne (London 1930), Vol. 1, 175Google Scholar.

¹³ A similar phenomenon seems to be discernible in the internal politics of the Third French Republic, where the Center, represented in particular by the Radical party, held the balance between Right and Left. The party would govern for a time with the support of the clericalists, until its rank and file reacted against this coalition. Then it would lean on the support of the socialists for a time, until the Radical rank and file reacted against that. By throwing their weight now to the Right, now to the Left, the Center politicians managed to maintain the system through a number of repeated oscillations, an “ever-recurring cycle” in the words of Siegfried, Andre (Tableau des partis en France [Paris 1930], 126Google Scholar).

¹⁴ Bolingbroke, , Works (Dublin 1793), Vol. II, 372–73Google Scholar. David Hume remarked, in a similar vein: “Our wars with France have been begun . . . from necessity; but have always been too far pushed from obstinacy and passion” (“Of the Balance of Power,” in Essays and Treatises on Several Subjects [Basel 1793], Vol. II, 99)Google Scholar.

¹⁵ P. 23; see p. 436, n. 19, for Gregory King's statistics.

¹⁶ A great number of favors and places in all parts of the country were at the disposal of the Crown, constituting a very effective means of influence at election time. As Lord Chancellor Cowper wrote to Anne's successor shortly after her death: “Give me leave to assure your Majesty, on repeated experience, that the parties are so near an equality, and the generality of the world so much in love with the advantages a King of Great Britain has to bestow without the least exceeding the bounds of law, that it is wholly in your Majesty's power, by showing your favour in due time [before the elections] to one or other of them, to give which of them you please a clear majority” (Trevelyan, 213).

¹⁷ 6.5 = 10—½·7. The constants in this formula, 10 and ½, are expressions of the permanent attitudes behind the repeated reactions of British voters during the period in question. It is conceivable that a similar formula could be found to describe French political reactions during the Third Republic (cf. n. 13 above), but then not only the variables but also the constants would be different. Similarly, in economics, the demand for two different commodities may be described by the same kind of formula, but as a rule the constants will be different.

¹⁸ Trevelyan, III, 45; cf. II, 169.

¹⁹ As has been intimated, Queen Anne did not always succeed very well in using her influence to keep the parties balanced, especially not toward the end of her reign. This is consonant with the shape of Figure 2, in which the cobweb moves away from the equilibrium position, the swings becoming more violent as time passes, while in Figure 1 there is apparent a tendency to convergence toward the point of equilibrium and a concomitant dampening of the swings.

No doubt voting in Anne's time was also influenced by factors other than those I have mentioned, factors that can be called extraneous to the system. Similar phenomena are well known in economic life. A cobweb model represents the mutual interplay of sellers' and buyers' reactions, with no allowance being made for factors such as changes in weather conditions, which often play an important role. An extraneous factor of this kind may decisively influence the size of a crop, perhaps to the extent of completely changing the cobweb picture.

We know that the mood of the British voter in the early years of the War of the Spanish Succession was influenced in part by a series of exceptionally good harvests. However, this factor was probably not of decisive importance.

²⁰ Trevelyan, III, 90.

²¹ The actors themselves to a large extent operated with quantitative notions. Th e French frontier fortresses had such strength, it was held, that the Allies must outnumber the French troops by some 25,000 men to obtain equality. A yearly British subsidy of £250,000 was reckoned as roughly equivalent to an army of 25,000 mercenaries, mostly men hired from petty German princes. See The Cambridge Modern History (Cambridge 1908), Vol. V, 414, 418Google Scholar. Statesmen tried to evaluate the balance of power as much as possible in quantitative terms. Thus the Partition Treaties of 1698 and 1700 were based on the idea of preserving the balance by dividing the Spanish Empire inheritance according to certain numerical calculations, as acknowledged, for instance, by Louis XIV in a letter of February 1699 giving instructions to his ambassador in London (ibid., 388). However, when the whole of the Spanish Empire fell to his grandson, Louis put aside the thought of equilibrium.

²² In the classical theory of monopoly, it is assumed that while one individual can affect other individuals, none of them is strong enough to affect him. Under this assumption, as in the case of perfect competition, indeterminacy is again avoided. Th e actions of Queen Anne, when she presented the British electorate with inducements to vote this way or that, can be compared to the actions of a monopolistic seller manipulating his prices.

²³ “War Without Pain, and Other Models,” World Politics, XV (April 1963), 472Google Scholar.

²⁴ The relationship between one party and the voters could be termed a subsystem. See Young, Oran R., “A Survey of General Systems Theory,” General Systems, IX (1964), 69Google Scholar, in which a subsystem is defined as “an element or functional component of a larger system which fulfills the conditions of a system in itself but which also plays a specialized role in the operation of the larger system.”

²⁵ Hall, A. D. and Fagen, R. E., “Definition of System,” General Systems, 1 (1956), 23Google Scholar.

²⁶ A Systems Analysis of Political Life (New York 1965), 25Google Scholar.

²⁷ Parsons and others, Toward A General Theory of Action (Cambridge, Mass., 1951), 228, 231Google Scholar.

²⁸ Eckstein, 14–15, n. 8.

²⁹ Can we define, for instance, the limits of political stability in the French Third Republic? Eckstein argues (p. 228) that the regime was near the breaking point several times, such as during the Boulanger period. On the other hand, however, the Third Republic did survive both this and other severe crises; it came through the ordeal of a world war in which France bore die brunt of the fighting for four years. Its breaking point at any given moment is certainly not easy to determine. Eric A. Nordlinger says, “The outstanding characteristic of the French political system is its historical instability. . . . While the republic tottered on in the interwar period the life-span of its governments was calculated in terms of months rather than years . . .” (“Democratic Stability and Instability: The French Case,” World Politics, XVIII [October 1965], 127)Google Scholar. It is true that in the 1930's the reactions of voters at the polls as well as the rapid changes of ministries can be taken as indications of instability. The 1920's were different, however. Despite frequent changes of premiers, there was a great deal of continuity. From January 1921 until March 1932 French foreign policy was practically in the hands of no more than two men, Raymond Poincare and Aristide Briand. But then came, in rapid succession, Paul-Boncour, Barthou, Laval, Flandin, Deibos, Bonnet, Daladier, and Reynaud as foreign ministers (see Craig, Gordon A. and Gilbert, Felix, eds., The Diplomats 1919–1939 [New York 1965], Vol. I, 52, Vol. II, 382Google Scholar).

³⁰ Gulick, 249. The final settlement at Vienna did not depend merely on this simple kind of arithmetic. The buffer states to the east of France, for instance, were created not only with a view to the number of their inhabitants; regard was also had for the defensibility of their frontiers, the existence of rivers and harbors that made it possible to bring them swift aid from across the sea, and so on (ibid., 259).

³⁰ Gulick, 249. The final settlement at Vienna did not depend merely on this simple kind of arithmetic. The buffer states to the east of France, for instance, were created not only with a view to the number of their inhabitants; regard was also had for the defensibility of their frontiers, the existence of rivers and harbors that made it possible to bring them swift aid from across the sea, and so on (ibid., 259).

³¹ Cf., for instance, Taylor, Lee and Glasgow, Charles W., Occupations and Low-Income Rural People (Baton Rouge 1963Google Scholar); and Olson, Mancur Jr., “Agriculture and the Depressed Areas,” Journal of Farm Economics, XLVI (December 1964), 984.CrossRefGoogle Scholar

³² See Huntington, Samuel P., “Arms Races: Prerequisites and Results,” Public Policy, VIII (1958Google Scholar), 50f., for this and other examples of what he terms absolute, as opposed to relative, armaments goals (i.e., goals relative to the armaments of other nations).

³³ (New York 1957).

³⁴ “Stability in Competition,” Economic Journal, xxxix (March 1929), 54–55Google Scholar.

³⁵ See, in particular, Hermens, F. A., Democracy or Anarchy? (Notre Dame 1941Google Scholar).

³⁶ “Optimum Location in Spatial Competition,” Journal of Political Economy, XLIX (June 1941), 423Google Scholar.

³⁷ P. 120.

³⁸ Brenan, Gerald, The Spanish Labyrinth (Cambridge 1943), 266Google Scholar. The law of 1932 was applied only twice. Th e overall result of the 1933 elections was a very sharp swing to the Right. Then came a no less violent swing to the Left at the 1936 elections. Shortly afterward the Civil War broke out.

Arrangements in France had the opposite effect of increasing the parliamentary representation of the Center at the expense of the extremes. It is sometimes said that this was due to the two-ballot system, which made voters switch to the support of what they regarded as the lesser evil at the second ballot (Duverger, Maurice, L'influence des systèmes électoraux sur la vie politique [Paris 1950Google Scholar], 44: “Car le plus grand nombre des élus du centre ont triomphé au deuxième tour, les uns grace a l'appui de la droite, les autres grâce à l'appui de la gauche”). A more important factor, however, seems to have been the extensive gerrymandering carried out to reduce the influence of many industrial districts in favor of the Center's rural strongholds. On the French elections of 1928, 1932, and 1936, see Lachapelle, Georges, Les régimes électoraux (Paris 1934), 160Google Scholar, 164; and articles by Sharp, Walter R. in American Political Science Review, xxii (August 1928), 685Google Scholar–86, and xxx (October 1936), 868.

In Imperial Germany the two-ballot system worked mainly against the Left (see Duverger, Political Parties, 2nd English ed. [London 1959], 375, fig. 44), an effect produced not by the second ballot as such but by an old-fashioned apportionment of seats favoring the rural districts at the expense of the industrialized constituencies, which found themselves increasingly underrepresented as the urban population grew in numbers. A similar development took place in Norway, where the two-ballot system was also in operation at that time (Debate in the Norwegian Parliament, Forhandlinger i Stortinget, November 27, 1919). In both Germany and Norway, the phenomenon of rotten boroughs was more important than the two-ballot device.

³⁹ See my article “Wahlsoziologische Probleme des Nationalsozialismus,” Zeitschrift für die gesamte Staatswissenschaft, cx, No. 2 (1954), 282Google Scholar–83; and Hermens, 257.

⁴⁰ (Boston 1963).

⁴¹ Ibid., 285, 281.

⁴² Ibid., 26. Rosecrance confines his detailed discussion to the years 1740–1789, but he repeatedly refers to the first part of the eighteenth and the latter part of the seventeenth century as belonging to the same system. For instance, on page 22, he mentions the battles of the War of the Spanish Succession. On page 234, he says that the eighteenth century never witnessed “any fundamental or persistent attempts to destroy the pattern of international outcomes like those which occurred in the first part of the seventeenth and nineteenth centuries. Neither the international system nor the internal constitution of its various actors was ever at stake.”

⁴³ Ibid., 283.

⁴⁴ On Maryborough's plan, see Trevelyan, II, 368. I believe Bernard Brodie is right in speaking about the “myth” of the limited character of warfare in the eighteenth century. See his Strategy in the Missile Age (Princeton 1959), 30Google Scholar.

⁴⁵ P. 229.

⁴⁶ Cf. the articles by Ash, Maurice A.,Kaplan, Morton A., and Lee Burns, Arthur in Part IV of Rosenau, James N., ed., International Politics and Foreign Policy (New York 1961), 334Google Scholar–66; Deutsch, Karl W. and Singer, J. David, “Multipolar Power Systems and International Stability,” World Politics, xvi (April 1964), 390–406CrossRefGoogle Scholar; Waltz, Kenneth N., ‘The Stability of a Bipolar World,” Daedalus (Summer 1964), 881–909Google Scholar; and Rosecrance, R. N., “Bipolarity, Multipolarity, and the Future,” Journal of Conflict Resolution, x (September 1966), 314CrossRefGoogle Scholar–27. It should be noted that a bloc which appears monolithic may conceal internal cleavages. On the other hand, an apparently many-sided constellation can often be reduced to a simpler form. There were many actors in the wars against Louis XIV: Besides the various large and small states there were groups like the Protestant rebels in France, Italy, and Hungary; French Huguenot refugees; English and Irish Catholic refugees; and Spanish guerrillas fighting for or against rival pretenders. There was the Pope, who played an independent role, and there was also the Jesuit Order, parts of which acted independently of the Pope. Yet in the end, from all these diverse elements there emerges a three-unit pattern: on the one hand, Louis XIV and his clients; on the other hand, Austria and her continental helpers; and thirdly, the decisive balancer, Britain.

William H. Riker takes up the question of the size of a coalition in his Theory of Political Coalitions (New Haven 1962), 211Google Scholar. Riker states as a fundamental principle that coalitions will “tend toward the minimal winning size.” This is certainly often true in domestic affairs (cf. Schattschneider, E. E., Party Government [New York 1942], 95Google Scholar). However, in international politics the model is less applicable. At Yalta, in early 1945, the Western Allies were confident of winning the war against Japan, but nevertheless the USSR was brought in to enlarge the coalition. Though this meant sharing the spoils with an extra participant, it also seemed to promise a substantial reduction in the cost of achieving victory.

⁴⁷ There was evident “une tendance profonde à se diviser en deux grandes fractions rivales,” “deux tempéraments politiques fondamentaux,” “une opposition de base entre la Droite et la Gauche, l'Ordre et le Mouvement.” Odier differences were only “oppositions secondaires à l'intérieur de chaque groupe d'opinions” (L'influence des systèmes electoraux, 42–43).

⁴⁸ Pp. 215–16.

⁴⁹ Ibid., 232. Perhaps the notion of overlapping cleavages could also be applied in an analysis of the Third Republic. Duverger seems to regard the political scene as essentially bipolar in that period; no doubt it contained many units, but a simple pattern of two great rival factions emerged on more important occasions. Though the Chamber of Deputies displayed a somewhat confusing array of party groups, he says, most of them could be arranged without too much difficulty along a Right-Left continuum. Even if one accepts this statement, however, it is hard to see the regime of the Third Republic as a two-unit system. It represents rather a variation on the three-unit theme (I would say a variation of die political cobweb type; see n. 13 above). A special case of overlapping cleavage is also to be noted. Th e French Right was clerical and capitalist; die Left, anticlerical and socialist. In the Center, the cleavages overlapped, the Radicals being capitalistic and anticlerical—rightist in economic matters, leftist in religion—putting the main emphasis sometimes on their opposition to socialism and sometimes on their opposition to clericalism.

⁵⁰ Some empirical research in this direction has already been undertaken. For instance, Alfred Winslow Jones, who studied an American industrial city in the 1930's with the aid of systematic interviews, found a tri-modal distribution of opinion corresponding to the attitudes of big business, labor, and the middle class. See his Life, Liberty, and Property (New York 1941), 327Google Scholar. Cf. Key, V. O., Public Opinion and American Democracy (New York 1961), 70–73Google Scholar. For attempts to measure the strength of “overlapping cleavages” with election statistics and survey data, see Rokkan, S. and Valen, H., “Regional Contrasts in Norwegian Politics,” in Allardt, E. and Littunen, Y., eds., Cleavages, Ideologies and Party Systems (Helsinki 1964Google Scholar); and Rokkan, S., “Geography, Religion, and Social Class: Cross-Cutting Cleavages in Norwegian Politics,” in Lipset, S. M. and Rokkan, S., eds., Party Systems and Voter Alignments (New York 1967Google Scholar). Cf. Dahl, Robert A., Pluralist Democracy in the United States (Chicago 1967), 338Google Scholar–70. Truman, David B., The Governmental Process (New York 1962), 508Google Scholar–10, uses the somewhat related concept of “overlapping membership” in groups. For an incisive criticism of Truman, see Olson, Mancur Jr., The Logic of Collective Action (Cambridge, Mass., 1965), 124Google Scholar.