29. Multipolar Power Systems andInternational Stability*

Karl W. Deutsch and J. David Singer combine their tal-ents here to probe the implications of recent changes in the structure of globalpolitics for the stability of the international system. Unlike the previous selection,this one presumes that bipolarity no longer marks systemic structure and that ashift toward multipolarity has occurred. While noting that the short-run implica-tions of this shift may be considerable, Professors Deutsch and Singer are dubiousabout the proposition that in the long run the shift will result in a more stableworld order. [Reprinted from World Politics, XVI (1964), 390-406, by per-mission of the authors and the publisher.]

In the classical literature of diplomatic history,the balance-of-power concept occupies a centralposition. Regardless of one's interpretation of theterm or one's preference for or antipathy to it, theinternational relations scholar cannot escape dealingwith it. The model is, of course, a multifaceted one,and it produces a fascinating array of corollaries;among these, the relationship between the numberof actors and the stability of the system is one of themost widely accepted and persuasive. That is, as thesystem moves away from bipolarity toward multi-polarity, the frequency and intensity of war should beexpected to diminish.

To date, however, that direct correlation hasnot been subjected to rigorous scrutiny by eitherabstract or empirical test. For the most part, it hasseemed so intuitively reasonable that a few historicalillustrations have been accepted as sufficient. This is,on balance, not enough to support a lawful generaliza-tion; it must eventually be put to the historicaltest. This will be done eventually,' but in the interim

* Research used in this article has been supported inpart by the Carnegie Corporation.

1 Data-gathering on this topic is currently beingcarried on by David Singer.

this hypothesis should at least be examined on formal,abstract grounds. The purpose of this article, there-fore, is to present two distinct—but related—linesof formal, semi-quantitative, argument as to whythe diffusion-stability relationship should turn outas the theoretician has generally assumed and as thehistorian has often found to be the case.

I. A Probabilistic Concept ofInternational Political Stability

Stability may, of course, be considered from thevantage point of both the total system and theindividual states comprising it. From the broader,or systemic, point of view, we shall define stability asthe probability that the system retains all of itsessential characteristics; that no single nation be-comes dominant; that most of its members continueto survive; and that large-scale war does not occur.And from the more limited perspective of theindividual nations, stability would refer to theprobability of their continued political independenceand territorial integrity without any significantprobability of becoming engaged in a "war for

315

316 Theories of Balance and Imbalance

survival." The acceptable level of this probability—such as 90, or 95, or 99 per cent—seems to beintuitively felt by political decision-makers, withoutnecessarily being made explicit, but it could beinferred by investigators in the analysis of particularcases. A more stringent definition of stability wouldrequire also a low probability of the actors' becomingengaged even in limited wars.

This probabilistic concept of political stabilitydiffers from the stability concept used by L. F.Richardson, which was that of classical mechanics.Richardson's stability referred simply to any set ofconditions under which the system would return toits equilibrium state; instability meant to him anystate of affairs that would not so return, but ratherwould continue to change until reaching some limitor breakdown point of the system. A low rate ofexponential growth of arms expenditures, of twocompeting powers—say, of 2 to 4 per cent a year—would be "unstable" in Richardson's terms, butmight be compatible with a political stability for theindefinite future, as long as national per capitaincome or other indicators of the system's absorptioncapacity grew at least at the same rate. In that case,of course, the per cent for defense taken from theaverage per capita income would remain unchangingor might decline, with no untoward effects upon theinternal financial or political stability of the statesconcerned—or upon the stability of the relationbetween them, as long as both continued to grow atsimilar rates.2

Richardson's essentially non-political stabilityconcept and the political and probabilistic conceptproposed here will lead to more closely similarresults, however, if we reformulate Richardson'sincrements of arms expenditure of two rival statesnot in terms of dollars but in terms of per cent ofnational income. An arms race proper would thenbe defined as one in which the rival states stimulateone another to divert increasing proportions of theirnational income to military preparations—a practicewith obvious political and economic limits, wellbefore the entire 100 per cent of national income isconsumed by military spending. The chief practicalcase investigated by Richardson, the arms race

2 This argument does not take into account, of course,the effects of any radical changes in the quantity or effective-ness of weapons, or of the quantitative increase of currentlyavailable weapons of mass destruction to very high levels.

preceding World War I, was in fact of this nature, ,-Jsince the growth rate of the aggregate arms budget {of the two main coalitions was of the order of 15 percent per year, in contrast to income growth ratesof the order of only 5 per cent in the principalcountries.

The political definition of equilibrium that wehave just proposed is quite compatible with thelanguage used by Morton Kaplan.3 In Kaplan'sformulation, equilibrium and stability can be definedonly in terms of particular variables, which must bechosen in advance. Thus, if we focus our attentionupon the absolute level of armaments—say, in termsof a constant dollar expenditure at constant prices—the system would be stable, and a system in which therival powers allocated constant proportions of theirgross national products to armaments would appearto be unstable in these terms. If, however, thesepercentages of GNP themselves were chosen as thecritical variables, the system would once againappear as stable.

The rest of this article will be presented in foursections. In the first, we link up the independentvariable (number of independent actors) with thedependent one (stability of the system) by means ofan emphasis on "interaction opportunity"—ourintervening variable. In the second section, the inter-action opportunity concept is extended to the pointwhere it impinges on the degree of attention thatany nation in the system may allocate to all of theother nations or to possible coalitions of nations.In the third, the multipolar and bipolar models areconnected with Richardson's model of arms racesand similar kinds of escalating conflicts. In the finalsection, these arguments are subjected to a new

3 Morton A. Kaplan, System and Process in Inter-national Relations (New York, 1957), 6-8. Kaplan hasformalized many classic formulations of balance-of-powertheory. For outstanding examples of these, see HansMorgenthau, Politics Among Nations (3rd edn., New York,1960), 167-226; Inis Claude, Power and InternationalRelations (New York, 1962), 11-93; Frederick L. Schuman,International Politics (6th edn., New York, 1958), 70—72,275-78, 577-79, 591-92; Arnold Wolfers, Discord andCollaboration (Baltimore 1962), 117-32; and QuincyWright, A Study of War (Chicago, 1942), II, 743-46. Forother attempts at formalization, see George Liska, Inter-national Equilibrium (Cambridge, Mass., 1957), 23-56,187-202; Edward V. GuJick, Europe's Classical Balanceof Power (Ithaca, 1955); and, for significant recent con-tributions, Anatol Rapoport, Fights, Games and Debates(Ann Arbor, 1960), and Richard Rosecrance, Actionand Reaction in World Politics (Boston, 1963).

[29] Multipolar Power Systems and International Stability 317

scrutiny, with the time scale introduced as a limitingfactor.

II. The Accelerated Rise ofInteraction Opportunities

The most obvious effect of an increase in the numberof independent actors is an increase in the number ofpossible pairs or dyads in the total system. Thisassumes, of course, that the number of independentactors is responsive to the general impact of coalitionmembership, and that as a nation enters into thestandard coalition it is much less of a free agent thanit was while non-aligned. That is, its alliance partnersnow exercise an inhibiting effect—or perhaps evena veto—upon its freedom to interact with non-alliance nations.

This reduction in the number of possible dyadicrelations produces, both for any individual nationand for the totality of those in the system, a corres-ponding diminution in the number of opportunitiesfor interaction with other actors. Although it mustbe recognized at the outset that, in the internationalsystem of the nineteenth and twentieth centuries,such opportunities are as likely to be competitiveas they are to be cooperative, the overall effect isnevertheless destabilizing. The argument is nothingmore than a special case of the widely employedpluralism model.

In that model, our focus is on the degree to whichthe system exhibits negative feedback as well ascross-pressuring. By negative—as distinguishedfrom positive or amplifying—feedback, we refer tothe phenomenon of self-correction: as stimuli in oneparticular direction increase, the system exhibits adecreasing response to those stimuli, and increasinglyexhibits tendencies that counteract them. This is theself-restraining system, manifested in the automaticpilot, the steam-engine governor, and most integratedsocial systems, and it stands in contrast to the self-aggravating system as seen in forest fires, compoundinterest, nuclear fission, runaway inflation ordeflation, and drug addiction.4

The pluralistic model asserts that the amplifyingfeedback tendency is strengthened, and the negativefeedback tendency is weakened, to the extent thatconflict positions are superimposed or reinforcing.

4 For an application of these and related conceptsto a range of political questions, see Karl W. Deutsch,The Nerves of Government (New York, 1963).

Thus, if all clashes and incompatibilities in the systemproduce the same divisions and coalitions—if allmembers in class Blue line up with one another andagainst all or most of those in class Red—the line ofcleavage will be wide and deep, with positive feed-back operating both within and between the twoclasses or clusters. But if some members of classBlue have some incompatible interests with othersin their class, and an overlap of interests with someof those in Red, there will be some degree of negativeof self-correcting feedback both within and betweenthe two classes.

This notion is analogous to that of cross-cuttingpressure familiar to the student of politics. Here weobserve that every individual plays a fairly largenumber of politically relevant roles and that most ofthese pull him in somewhat different attitudinal,behavioral, and organizational directions. Forexample, if an individual is (i) a loving parent, (2) amember of a militant veterans' organization, (3)owner of a factory, and (4) a Catholic, the first andthird factors will tend to deflect him toward a"coexistence" foreign policy, the second will pullhim toward a "holy war" orientation, and hisreligious affiliation will probably (in the 1960*8)produce a deep ambivalence. Likewise, followingRalf Dahrendorf's formulation, if status differenceis a major determinant of conflict exacerbation, andan individual is head of a family, a bank teller, andpresident of the lodge, he will coalesce with andagainst different people on different issues.5 Ineach of these cases, his relatively large number ofinteraction opportunities produces a set of cross-pressures such as largely to inhibit any superimposi-tion or reinforcement. The consequence would seemto favor social stability and to inhibit social cleavage;increasing differentiation and role specialization inindustrial society has, in a sense, counteracted theMarxian expectation of class warfare.

Thus, in any given bilateral relationship, arather limited range of possible interactions obtains,even if the relationship is highly symbiotic. But asadditional actors are brought into the system, therange of possible interactions open to each—andhence to the total system—increases. In economics,this accretion produces the transformation from

5 Ralf Dahrendorf, "Toward a Theory of SocialConflict," Journal of Conflict Resolution, II (June 1958),176-77.

318 Theories of Balance and Imbalance

barter to market, and in any social setting it producesa comparable increase in the range and flexibilityof possible interactions. Traditionally, social scien-tists have believed—and observed—that as thenumber of possible exchanges increases, so does theprobability that the "invisible hand" of pluralisticinterests will be effective. One might say that one ofthe greatest threats to the stability of any impersonalsocial system is the shortage of alternative partners.

If we assume, then, that any increase in thenumber of independent actors is conducive to stabil-ity, the question remains as to the quantitativenature of this correlation. Is there any particularlevel at which the system cannot be made morestable by the addition of new actors, or less stableby the loss of existing actors ? Is there, furthermore,some critical level at which small changes becomecrucial ? Our response must be based, of course,on the degree to which each single increment ordecrement affects the number of possible dyads,or bilateral interaction opportunities, in the system.That effect is found by applying the standard formu-i f -ui • N(N-i) . . .la for possible pairs: —i———-; thus, in a purely bi-

polar system, only one dyad or pair is possible, whilea tripolar situation produces three pairs, four actorsproduce six pairs, five produce ten possible pairings,and so on, as shown in Fig. i.

This figure indicates rather dramatically thedegree to which the number of independent actors

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affects the possible number of dyads, and thusinteraction opportunities. Even as we move frombipolarity to a tripolar system, the interactionopportunities within the system triple, and whenanother single actor is added the possible dyadicrelations increase by three, and so on, with eachaddition in the actor column producing an incrementof N—i in the interaction opportunity column.Intuitively, the student of international politics wouldnote that until N reaches five, there is an insufficientnumber of possible dyads, and that beyond thatlevel the stability-enhancing increment begins togrow very sharply.

So far, we have operated from the conservativeassumption that all nations have identical interests,concerns, and goals, and though we would not wantto exaggerate in the opposite direction, one cannotoverlook the diversity that does exist. A landlockednation can hardly offer fishing rights in its coastalwaters, an agricultural surplus nation will seldompurchase those same foodstuffs, two underdevelopednations are most unlikely to exchange machine tools,and a permanent member of the Security Councilcannot be expected to give much for assuranceof a seat in that organ. Every nation's needs andsupplies differ, and the more nations there are, thegreater will be the number and diversity of trade-offs available to the total system. As possible trade-offs increase, the greater the possibility for compensa-tory and stabilizing interactions to occur. That is,in a system characterized by conflict-generatingscarcities, each and every increase in opportunitiesfor cooperation (i.e., to engage in a mutually advan-tageous trade-off) will diminish the tendency to pur-sue a conflict up to, and over, the threshold of war.

Finally, membership in an alliance not onlyexercises a negative quantitative impact on a nation'sinteraction opportunities, but affects the quality ofthose that do continue to exist. On the one hand, thepattern-maintenance needs of the alliance will besuch as to minimize (a) the range of issues over whichit will conflict with an alliance partner, and (b) theintensity of such intra-alliance conflicts as arepermitted. On the other hand, the establishment ofsuch a clear-cut ingroup-outgroup division can onlylead to an increase in the range and intensity of anyconflicts with non-alliance actors.

To summarize, one logical explanation for thecorrelation between number of independent actors

[29] Multipolar Power Systems and International Stability 319

and the probability of armed conflict lies in the realmof enhanced interaction opportunities, observed interms of their quantity, diversity, and qualities.

III. The Accelerated Diminution inthe Allocation of Attention

A second line of argument that should also supportthe hypothesized correlation between multipolarityand stability revolves around the notion of attentionavailable for conflict. Here we assume that, as thenumber of independent actors in the system increases,the share of its attention that any nation can devote toany other must of necessity diminish. The argumentneed not, of course, postulate that each additionalactor will attract an equal share of the attention ofeach of the other actors, or necessarily attract thesame share as those already in the system. That sharewill be a function of many considerations and mayvary rather widely. Let us assume, then, that anynation's total external attention—that is, its in-formation-processing and resource-allocating ca-pabilities—will be distributed among all others inthe system according to a normal distribution, asillustrated in Fig. 2.

In this figure, we suggest that a very few of thetotal number of actors in the system receive verylittle of A's attention, that most of them receive amoderate share of that attention, and that a veryfew receive an impressively heavy share of it. Butregardless of the shape of this attention distributioncurve, the fact is that every actor claims some.

If those receiving a minimal share of A'sattention were to disappear into a coalition, thiswould have only a minor impact on the amount ofattention now left over for A to redistribute among theremaining independent actors. But if coalition were

Per centof Actors

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Figure 2. Share of attention

to occur among some of those receiving a greatershare of that original attention, A would then be ableto deal with the members of that coalition with fewerdemands on its information-processing and energy-allocating capabilities; as a consequence, thatremaining for allocation to the other actors in thesystem would be appreciably increased.

Now the limited attention capability of eachnation in the system must be allocated betweentwo different sets of relationships. First prioritywill tend tp go to all of those dyadic relationships inwhich it is a partner, while the dyads of which it isnot a member will receive a lesser, but not insignifi-cant, degree of attention. Some recent illustrations ofthis latter demand might be found in the attentionwhich the United States has expended on the Soviet-Yugoslavian, British-Egyptian, or Indian-Pakistandyads, or which the U.S.S.R. devoted to the Arab-Israeli, Cuban-American, or Franco-Algerian pair-ings. Regardless of membership or non-membership,each nation must spread its attention among mostof the dyads in the system.

What, then, is the effect of any trend toward oraway from bipolarity upon that distribution ofattention ? In Fig. 3, we plot that distribution accord-ing to the assumption that, with each single additionto the number of independent actors, the totalnumber of dyads in which nation A is a member willalso increase by one, following the formula N—i.

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320 Theories of Balance and Imbalance

With each increment in the number of dyads ofwhich A may be a member, the amount of attentionavailable for any one such pairing will drop, asshown in the upper (solid line) curve. Thus threeactors produce two possible dyads that include A,with an average of 50 per cent of A's attentionavailable for each; four actors produce three suchpairs and 33 per cent of A's attention for each; andfive actors produce four A-inclusive dyads, withonly 25 per cent of his attention available to each.

When we drop the condition that only thosedyads of which A (any actor) is a member canconstitute a drain on A's attention, and assume thatevery possible dyad will make some such demand,the attention curve responds even more rapidly toan increase in the number of independent actors.As the lower (dotted line) curve indicates, each newactor increases the total number of dyads by the

—-——- formula, as already used earlier in Fig. i,

with the percentage of share of attention availableto each dyad dropping even more sharply.

Why should these rapid decreases in per-centage of available attention exercise any effectupon the stability of the system ? In communicationtheory, it is generally recognized that below a certainsignal-to-noise ratio, the signal is essentially un-detectable; that is, it loses prominence as its strengthvis-a-vis the noise (or random disturbance) in thesystem diminishes. The same general principlewould seem to apply to social interaction; as Rapo-port and Schelling have pointed out, interactionbetween any two nations may be viewed as a specialcase of the interchange of messages between them.6Each state in this case would have to treat the mes-sages from its most prominent adversary of themoment as the signal relevant to this incipient conflictin or before its early stage of escalation; and it wouldtend to treat all other messages, concerning allother pairs of states, as noise of relatively littlerelevance to this particular conflict.7

The general requirement of at least a minimalsignal-to-noise ratio would then hold for this incipientconflict, as it would hold for any other communica-tion process; and we shall assume that it is approxi-

6 Rapoport, 213-22; Thomas C. Schelling, TheStrategy of Conflict (Cambridge, Mass., 1960), 83—118.

7 Cf. Colin Cherry, On Human Communication: AReview, a Survey, and a Criticism (Cambridge-New York,1957), 42 and passim.

mated by the ratio of governmental attention toforeign messages from this particular rival, to allother messages concerning other states or pairs ofstates. Just what this signal-to-noise ratio—or,here, minimal attention ratio—would have to be isa question of empirical fact. Signal-to-noise ratiosof i oo: i are not uncommon in electronic communica-tion systems. It is perhaps not excessive to assumethat the minimal attention ratio for an escalatingconflict would have to be i :g, since it does not seemlikely that any country could be provoked very farinto an escalating conflict with less than 10 per centof the foreign policy attention of its governmentdevoted to the matter.8

If we require a minimal attention of 10 per centfor an escalating conflict, the likelihood of suchconflicts thus will decline sharply with the decline ofthe average attention that any one government hasavailable for any one of the remaining actors in theinternational system.

The decline of this average available attentionwith an increasing number of actors in the systemhas been graphed in curves A and B in Fig. 3, asdiscussed earlier. We can now show on the samegraph the lines of minimal attention ratios required topermit average probabilities of, say, 20, 10, or 5 percent for an escalating conflict between any two actorsin the system. Several such lines, at the 10, 20, 30 ...per cent levels of an assumed minimum attentionratio, have been drawn in Fig. 3. Their intersectionswith curves A and B show how quickly the increaseof the number of actors will remove an internationalsystem from the danger zone, or how fast a diminu-tion in the number of actors will increase the averagerisk of escalating conflict among the remainder.

As far as it goes, this graphic representationconfirms the greater stability of multipolar systems,and it suggests some quantitative findings. It showsthat the average share of available attention for anyone conflict drops sharply as soon as there are morethan three power centers in the system, and moregently after there are more than five such centers;and it further suggests that the stability of the systemmay depend critically on the critical attention ratio—that is, on the proneness of countries to enter into

8 For an earlier version of a related argument aboutmass attitudes to quarrels with a foreign country, seeKarl W. Deutsch, "Mass Communication and the Lossof Freedom in National Decision-Making," Journal ofConflict Resolution, I (July 1957), 200-11.

[29] Multipolar Power Systems and International Stability 321

escalating conflicts even if only a small part of theirgovernment's attention is engaged in this particularquarrel.

Thus, if some minimum percentage of a nation'sexternal attention is required for that nation toengage in behavior tending toward armed conflict,and the increase in number of independent actorsdiminishes the share that any nation can allocateto any other single actor, such an increase is likelyto have a stabilizing effect upon the system.

IV. Some Implications for Richardson'sModel of Escalating Conflict

The task of this section will be to correlate thepropositions concerning the greater stability ofmultipolar systems in international politics, especiallyas recently formalized by Morton Kaplan, with theRichardson model of conflict;9 and to show that theformer proposition can be treated as a special caseof the general Richardson model.

In the Richardson model of the arms race, orof similar competitive relations, conflict behaviorof each of two parties is seen as growing at anexponential rate, similar to the growth of compoundinterest or to the progress of an explosion. The rateof this growth is described by a pair of differentialequations in which one party's increase in arma-ments—or of other competitive behavior—is per-ceived as a threat and becomes the motivating inputfor the corresponding reciprocal or retaliatory re-sponse of the other. Thus, if country A had spent inthe previous year $90 million on armaments, whileits rival B had spent $100 million, and if A now triesto equal B and increases its armaments budgets from$90 million to |ioo million, and if country B, whichpreviously had spent $100 million, tries to maintainthe previous ratio of arms budgets, then B must nowspend $in million in the following year; whereuponA, if its rulers still aim at parity with B, will now in-crease its budget accordingly to $i 11 million, forcingB to defend its old proportionate lead by raising itsarms budget by $12.3 million to $123.3 million, sothat not only the absolute amounts but also the in-creases in arms spending on both sides are growing

9 Kaplan, 21—53; Rapoport, 15—47; and the sameauthor's essay, "L. F. Richardson's Mathematical Theoryof War," Journalof Conflict Resolution, I (September 1957),249-99. See also L. F. Richardson, Arms and Insecurity(Chicago, 1960).

in every round, and the arms race will accelerate inever-growing steps until some limit or breakdown isattained.

This simple model would hold equally forbipolar and multipolar systems. In the latter systems,one might imagine that it could apply to everypossible pair of nations in rivalry, and thus to 10pairs in a five-power system, to 15 pairs in a six-powerworld, and generally to N(N—1)/2 powers in anN-power system. If country A wanted at leastto keep its proportionate lead against each of itsrivals, it would have to maintain its level in anexponentially growing arms race with the mostquickly growing of these rivals, because this wouldautomatically increase its lead over all the rest. Ifall powers followed this type of policy, the totalpace of arms competition for all countries would beset by the fastest growing competitor.

This model, however, seems too simple. It maybe more reasonable to assume that a country is mostlikely to respond to an increase in the arms expendi-ture of a rival only in regard to that part which appearslikely to be deployed or directed against itself.

In the case of a bipolar world, this considerationwould make very little difference. The strongestcountry, A, would have to fear almost the full amountof the increment in the strength of the next strongestpower, B, since in this bipolar world the third andfourth ranking powers, C and D, and all the lesserpowers down to N, are almost negligible in theirstrength in comparison to A and B. These negligiblelesser powers would thus not require any significantallocation of B's resources to ensure against the riskof having to fight them, and practically all of B'sstrength would remain available for use against A,forcing A in turn to increase its own efforts to the fullextent required to maintain its own margin ofstrength in relation to B's growth.

Matters are quite different, however, in amultipolar world. In a four-power system, C andD, the third and fourth ranking nations, are alreadynearly as strong as A and B, the top and second-rankpowers. Accordingly, B may have to allocate morethan one-half of its resources—and of its incrementin these—to the possibility of having to fight Cor D, and thus B may have left less than one-halfof its increment for a credible increase in its threatagainst A. The effect on A's behavior, according tothe Richardson model, would be correspondingly

322 Theories of Balance and Imbalance

less, since A would have to raise its arms budgetonly to the extent needed to hold its proportionatelead in regard to one-half or less of B's increment inarms expenditure. The arms race in a completelyrational world would thus tend to be slower undermultipolar conditions than under bipolar ones.

A different line of reasoning suggests the sameresult. Richardson's original model assumed that themotivation for a state to try to maintain its pro-portionate lead over the arms level of another wasautonomously generated within the state itself.Once the national subsystems of the internationalpolitical system had this motivation, in Richardson'smodel, then the consequences of an escalating armsrace followed under the conditions that he specified.It was the competitive motivations of the nationalstates, in Richardson's thought, that produced thecompetitive character of the international system.Many writers on international politics, from Machi-avelli onward, have taken the opposite view. Thelarger system, they have maintained, is itself com-petitive to start with, in that it rewards appropriatecompetitive behavior and penalizes the failure tocompete by the pitiless elimination of the laggardsand the weak. Machiavelli's princes, Adam Smith'sbusinessmen, and Charles Darwin's animals all mustcompete for survival in their respective systems, onpain of being wiped out otherwise, regardless of theirsubjective motivation. In time, each of these systemsis expected to select for survival primarily thosesubsystems that have responded most adequatelyto its competitive pressure. Which rival subsystemhappened to exercise this competitive pressure at themoment is secondary in each of these theories. Ifthis particular rival had been absent, another wouldhave taken his place and served the same function ofoffering a compelling challenge to competitivebehavior.

This type of thinking has remained familiar inthe popular rhetoric of arms competition. The worldis such, the argument used to run—or the adversaryis such, it has run more recently—that "there is nochoice" but arms competition or national doomthrough surrender or defeat. Regardless of themotivations of its own people, its own politicalsystem, and its own decision-makers, any state insuch a situation must respond to the challenge of anarms race or else perish.

How strong is this externally derived pressure

upon a state to increase its own armaments for thesake of survival, regardless of any other values ormotivations produced by its domestic politicalsystem ? Clearly, it is proportional only to that partof the increment in a rival's armament that is notlikely to be balanced by a shift in alliances under abalance-of-power policy. In a bipolar world, a 10per cent increase in the arms spending of power Amust be answered by an equal increment in the armsof B, and the escalation process may then proceed at10 per cent increments for each cycle. In a world offour approximately equal powers, a rise in the armslevel of power A from 100 to no would give A'scoalition, I—consisting, say, of A plus C—only astrength of 210 against the rival coalition II, con-sisting of B and D, with a strength of 200. Thesuperiority of coalition I over coalition II would thusbe not 10 but only 5 per cent; the offsetting arma-ments needed by coalition II would only have to beof 5 per cent; the subsequent increments of theescalation would likewise be of this lesser order ofmagnitude; and escalation would proceed moreslowly.

In a similar six-power world, a 10 per centincrease in the armament of one power wouldcompel an increment of only about 3 per cent inthe arms spending of the three members of the rivalcoalition. A ten-power world in the same situationwould only be forced to a 2 per cent arms rise foreach of five powers. Generally, every increase in thenumber of powers would slow down the speed ofRichardsonian escalation.

If we drop the assumption of approximatelyequal powers in a multipolar world, the same generalresult follows. So long as most powers are free tomove laterally from one coalition or alignment toanother, their self-interest will favor such balance-of-power policies as to produce very nearly evenlymatched coalitions, each of them composed quitepossibly of members of unequal power. In such amobile multipolar world, no government needs tofear a moderate decline in national power as potential-ly disastrous. It can survive as a second-class poweras safely or precariously as it did as a first-class one,provided only that it joins in time the appropriatenew alliance or alignment. Arms increases by a rivalpower, which in a bipolar world might pose a fatalthreat, might call in a multipolar world for littlemore than a quick adjustment of alliances.

[29] Multipolar Power Systems and International Stability 323

V. Some Implications for theDiffusion of Nuclear Weapons

If an increase in the number and diplomatic mobilityof actors may slow down the process of arms escala-tion, it would by the same reasoning also slow downany process of de-escalation. Here, too, a one-sidedarms reduction in a two-power world may elicit anequal response by the other power, while in amultipolar world the effect of any such unilateralinitiative would be much weaker.

If we are chiefly interested in rapid de-escalation—that is, in partial or complete disarmament—amultipolar world may prove more intractable than abipolar one; and we may view the emergence ofFrench, German, Japanese, or Communist Chinesenational power with justified alarm. If we are mainlyconcerned, on the contrary, with preventing anyrapid escalation of the two-power arms competitionbetween the United States and the Soviet Union, ashift toward a multipolar world may appear prefer-able.

At this point, of course, the bare and abstractarguments pursued thus far become quite insufficient.In our analysis of alternative international powersystems we have abstracted from all other qualitiesof the states, governments, and national politicalsystems within them. At the point of policy choice,however, these hitherto neglected aspects may bethe decisive ones. A bipolar system in which each ofthe two rival powers is likely to be moderate andcautious in its policy initiatives and responses mightbe a great deal safer than a multipolar world contain-ing one or several well-armed powers whose govern-ments or politically relevant strata were inclined toincompetence or recklessness. As elsewhere, so alsoin international politics a stable general system couldbe wrecked by the introduction of unstable com-ponents.

At the present time, the importance of thislatter point may well be decisive. Each of the presentmajor nuclear powers—the United States, Britain,and the Soviet Union—has been politically stable,in the sense that each has retained its particular typeof government for over forty years. None of thesethree countries has been notable for initiating largeand reckless military enterprises. Among the middle-level and smaller powers most likely to press fornuclear weapons during the next decade—which

include France, Germany, Japan, Mainland China,Nationalist China, and perhaps Egypt and others—there are several whose recent history lacks anycomparable evidence of stability in domestic institu-tions and caution in international affairs. If thisstage should be followed by the dissemination ofnuclear weapons among a still larger number ofcountries, including inevitably at least some withstill less stable domestic regimes and less cautiousmilitary policies, the instability of the internationalsystem would be still more dangerous. For thesereasons, any successful efforts by the United Statesand other powers to slow down the dissemination ofnuclear weapons would tend to increase the stabilityof the international system. In the present article,devoted to an abstract argument, these matterscan only be indicated, but they must not be for-gotten.

One other problem, however, should be dis-cussed here: the time horizon under which thestability of international systems is evaluated. Amultipolar world, though often more stable in theshort run than a bipolar one, has its own problemof long-run political stability, and it is to this that wemust now turn our attention.

VI. The Long-run Instability ofMultipolar Systems

On the basis of these considerations, it might seemthat a multipolar system could last forever, or for avery long time, by always opposing the ambitionsof its currently top-ranking member; and this isindeed what some writers have claimed as a virtueof the balance-of-power system. In each of thesections above, however, we have dealt with con-siderations of an essentially short or middle-runnature, with a rather incomplete view as the naturalconsequence.

There are at least two analytic reasons why thisrelatively benign long-run outcome cannot beexpected. For one thing, if we accept the usual zero-sum assumption of Machiavelli and the classictheory of games—according to which any gain byone contender can occur only through an equalloss by one or more of his rivals—then we mustassume that each contending power ordinarily willtry to acquire all the territory and population it canat the expense of its rivals, and that it will do nothing

324 Theories of Balance and Imbalance

to create new rivals for itself. The model thus providesfor the possibility of the destruction of states whoserulers misjudged the precise balance of strength atthe moment, or whose economies and populations nolonger yielded the increasing increments in armsspending and military effort required by the com-petition, but this model does not provide for thecreation of new states. If the probability of statesperishing is small, but larger than zero, and theprobability of substantial new powers arising is zeroin terms of this model, then the model will predict adiminishing number of effective contenders, leadingeventually to a two-power world or to the survivalof a single power, as in the case of the reduction of themany governments of classic antiquity to the two-power clash of Rome and Carthage, and of Rome'sfinal long monopoly of power in the Mediterraneanworld until new forces entered from outside theregion.

The second line of reasoning is based on con-siderations of statistics. Thus far we have takenprobabilities only in terms of their central tendencies,rather than in terms of the variance of possible out-comes and their distribution. If we assume theseoutcomes to be normally distributed around somemean, then the usual outcome of an increment inthreat by power A against power B in a multipolarsystem will consist in both A's and B's rindingenough allies, respectively, to match the power oftheir respective coalitions and to produce the rela-tively moderate outcomes predicted by the classicbalance-of-power model. In rare cases, however,corresponding to one tail of the distribution, stateA will find a great preponderance of allies and becomeable to destroy its current enemy, B, completely;and in other rare cases—corresponding to the othertail of the distribution—A must expect to finditself facing an overwhelming coalition of adversariesthat will destroy it. In the short run, only the moderatecentral tendencies of the distribution of outcomes ofthe coalition-forming process will be frequent enoughto be taken into account, but in the long run thebalance-of-power world must be expected to produce

eventually dramatic and catastrophic changes, bothlocally and at last at the system level. The number ofyears after which long-run rather than short-runphenomena are likely to prevail will depend on thefrequency of international crises, and on the shapeof the distribution of balanced and unbalancedcoalitions, respectively, as outcomes of the coalition-forming process.

This expectation seems in good agreement withthe historical data. No balance-of-power systemhas lasted longer than a few centuries, and most ofthe original powers contending in such systemshave survived as independent powers only for muchshorter periods.10

The classic descriptive and analytical views oftwo-power confrontations and of the balance ofpower among several contenders have been formaliz-ed by several writers. The most prominent models, ofthe tight bipolar and multipolar world, respectively,can be interpreted in terms of the dynamic model ofconflict by Lewis F. Richardson. The results suggestthat the Richardson model, with very simple assump-tions, can be made to include the bipolar and multi-polar models as special cases. This combined modelthen suggests some general inferences in predictionsabout trends that appear to accord well with historicaldata. In the long run, according to this model, evenmultipolar systems operating under the rules ofbalance-of-power policies are shown to be self-destroying, but both in the short and the long runthe instability of tight bipolar systems appears tobe substantially greater. It seems plausible that, if thespread of nuclear weapons could be slowed down orcontrolled, a transition from the bipolar internationalsystem of the early I95o's to an increasingly multi-polar system in the 1960*8 might buy mankind somevaluable time to seek some more dependable basesfor world order.

10 For some historical data, see the discussion of thereduction of Italian city states during the years 1300—1537from 70 or 80 to 10, in A. J. Toynbee, A Study of History(London-New York 1945), III, 355-56; cf. also 301-4,345-48. In addition, see Wright, II, 762-63 ("The Dis-appearance of Small States").