A structural analysis of the situation in the Middle East in 19561

FRANK HARARY Research Center for Group Dynamics, The

Résumé (10) for groups of persons. It was antici- Heider and Newcomb We attempt to display a systematic ap- pated by (8) (11) with their toward balance&dquo; and proach for the distinction between states of &dquo;tendency &dquo;strain toward equilibrium and disequilibrium in the inter- symmetry,&dquo; respectively. More recently, an axiom system based on balance relationships between nations, using as cor- has been from which roborative material the rapid shifts in 1956 theory proposed (2) the assertions of Freud the among the various nations, brought about by (3) regarding an individual can the Middle Eastern situation. The psycho- development of the ego of be derived. From the logical theory behind this approach is that of logically general structural balance, which is pertinent in the approach of &dquo;systems theory&dquo; (9), the notion of balance verified present context to balance of power, while already experimentally the logical framework involves the mathe- (10) for groups of individuals, and then to the structure of the of a matical theory of graphs. We do not assert applied (2) ego well be considered that this theory in its present form is predic- single individual, might for larger systems than groups. This is similar tive, but we do feel that it offers a well- in to the work of Guetzkow The organized mode of thinking which, although spirit (4). purpose of this note is to propose the mathe- simple, may be fruitful. We also comment on matical theory of balance as a systematic some aspects of the Hungarian situation in approach to the interaction between nations. terms of structural balance. It must be borne We set the stage for the later discussion of in mind this article that it was throughout the international situation in terms of the written in early 1957 and that therefore the theory of structural balance by presenting a interrelationships among nations described brief outline of this theory on an intuitive herein reflect that time period. level. Fortunately, it is not necessary to be- Introduction come steeped in the mathematical details of the theory of graphs, but it is sufficient to be The of structural balance has theory ( 1 ) able to follow the argument with the assist- been tested in the laboratory psychological ance of the accompanying figures. In suc- ceeding sections we take up a rationale for 1 I am indebted to Anatol Rapoport for sug- balance to gesting this article and to Dorwin Cartwright for applying theory nations, examples making several helpful comments. of the tendency toward balance, the global 168 situation, desires and perceptions, the Hunga- Heider (8), reflecting the general field-theo- retical has considered certain rian developments, and a prediction attempt. approach, aspects of cognitive fields which contain perceived peo- In the applications of to ple and impersonal objects or events. His analy- between of our relationships pairs nations, sis focuses upon what he calls the P-O-X unit of discussion does not contain any conclusions a cognitive field, consisting of P (one person), 0 which are not deducible from a simple ( another person), and X (an impersonal entity). Each relation the of the unit is con- common sense postulate of polarity. Such among parts ceived as interdependent with each other rela- a polarity principle would assert that all tion. Thus, for example, if P has a relation of nations must be divided into two coalitions affection for 0 and if 0 is seen as responsible for in such a way that any two nations in the X, then there will be a tendency for P to like or same coalition are friendly and any two na- approve of X. If the nature of X is such that it would be evaluated as the whole tions from different coalitions are unfriendly. &dquo;normally&dquo; bad, P-O-X unit is placed in a state of imbalance, and This is very closely related to, but not com- pressures will arise to change it toward a state of identical with the structural theorem pletely balance. These pressures may work to change for balance which appears in the next section. the relation of affection between P and 0, the The principal difference lies in the word relation of responsibility between 0 and X, or the relation of evaluation between P and X. &dquo;structure.&dquo; For there may be indifference relationships between certain pairs of nations We now quote from Heider (8), whose which lie either in the same coalition or in basic hypothesis asserts that there is a ten- different coalitions. The polarity approach dency for cognitive units to achieve a bal- does not make this distinction. At present, anced state. Pressures toward balance may balance theory has not as yet been developed produce various effects: to the extent that it enables the handling of In the case of two entities, a balanced state structural situations in which the interna- exists if the relation between them is positive (or tional bonds have It is may varying strength. negative) in all respects.... In the case of three precisely this open problem area which holds entities, a balanced state exists if all three rela- the greatest promise for the evolvement of a tions are positive in all respects, or if two are and one theory which would be sufficiently compre- negative positive. If no balanced state exists, then forces towards hensive to be It is that predictive. very likely this state will arise. Either the dynamic charac- the of will be probability theory ters will change, or the relations will be changed involved. through action or through cognitive reorganiza- tion. If a change is not possible, the state of im- Balance Theory balance will produce tension. We now describe briefly the historical In the article, &dquo;Structural Balance: A Gen- background of balance theory and then dis- eralization of Heider’s Theory&dquo; (1), there is a cuss the modification for generalizing this brief summary of some of the major results of theory to nations from those entities for which the work of others who used Heider’s theory it has already been shown to be appropriate as a point of departure for further theoretical as a mathematical model. We begin by quot- and empirical work. ing a paragraph from Cartwright and Harary In Cartwright and Harary (2), there is ( 1 ) , which sets the stage for the generaliza- provided an application of balance theory in tion of Heider’s theory from a triad consisting which the entities are no longer persons and of two persons and one object to any number objects as in Heider’s theory, but are parts of entities regardless of the number of per- of a person’s personality, such as ego and id, sons and the number of objects. as well as &dquo;inner instinctual stimuli&dquo; together 169 with external stimuli, both pleasant and with some of the lines joining pairs of points. unpleasant. It is shown in (2) that the Thus the graph of Figure la has three points assertions of Freud (3) are derivable as and three lines. A ( Figure 1 ) logical consequences of an axiom system is a generalization of a graph in which some which includes as one of its postulates the of the lines are regarded as positive and the &dquo;tendency toward balance&dquo; which is stated remaining lines as negative. Signed graphs as an empirical hypothesis in the next section. are useful in providing a structural depiction We will assume throughout this paper that of a binary relation with both positive and nations are admissible entities for study by negative relationships (lines) between the the approach of the theory of structural bal- pairs of objects or entities (points) involved. ance and that the relation of alliance, cooper- The realization of signed graphs in the pres- ation, agreement, or other friendly behavior ent article takes points as nations, positive between a pair of nations is intrinsically posi- lines as friendship or alliance, and negative tive. This approach was implicitly antici- lines as hostility or warfare. For example, pated by Guetzkow (4). On the surface, the the four signed graphs of Figure 1 (in which conclusions to be drawn from this way of pre- solid lines are positive and dashed lines are senting international relations are not sur- negative ) contain 0, 1, 2, and 3 negative prising. Any common sense analysis would lines respectively. yield the same results. Of course it is desir- A signed graph is balanced if, and only if, able that a first rough approximation to all of its &dquo;cycles&dquo; are positive. The impor- reality using a mathematical model be con- tance of this concept lies in the following: sistent with common sense results. The prin- cipal idea which makes this approach more EMPIRICAL HYPOTHESIS (Tendency Toward than a collection of diagrams to portray a Balance) known situation is that the structure of inter- A balanced structure has greater stability national relations among several nations or than one which is not balanced. If a given groups of nations is made explicit. The par- structure is not balanced, there will be a ten- ticular manner in which nations are related dency to modify the structural bonds in order to each other may be positive, negative, indif- to achieve balance. There is both empirical ferent, or even sometimes ambivalent. This and theoretical justification ( 1 ) for this in a is discussed in more detail later section hypothesis. Other related tendencies are dis- which explicitly spells out several of the lim- cussed in the article (6). These include ten- itations of this theory in its present stage of dencies toward clustering, completeness, and development. positivity: Tendency Toward Balance Tendency Toward Clustering. If a collection of entities, having a relationship which is intrin- can be A graph (7) represented geometri- sically positive, has achieved balance, and if, cally by a set of points in the plane together furthermore, one of these entities is able to relo-

FIGURE 1 170 cate the remaining ones into subgroups, then the exclusive sets S and S! in such a way that entities will tend to be into two clusters realigned each positive line joins points of the same set in accordance with the structure theorem for bal- while each negative line joins two points ance. sets. Tendency Toward Completeness. A group from different structure will tend toward completeness, that is, This theorem gives insight into the nature if two entities are not yet interrelated in the of structural balance and in addition provides structure, then a bond will tend to be induced to a characterization of balance which is of between them. appear assistance in recognizing balanced structures. Tendency Toward Positivity. If a relationship In a directed the lines are a graph, directed is intrinsically positive, then any individual in - group will tend to show a marked preference to and AB denotes the line from A to B. The bonds rather than ones. forming positive negative convention (1) with regard to balance of a We note the emphasis in the statement of directed signed graph is that the direction of these last three tendencies that the relation- the lines be ignored. ship under consideration must be intrinsically In the next two sections, we represent positive. We have assumed that alliance or changing situations by a sequence of signed other cooperation or agreement between a graphs which present the structure at differ- pair of nations is intrinsically positive. ent times: to (initial time ) , tl, t2, etc. These In order to make the definition of struc- times are chosen in such a way that some tural balance precise, we require the follow- structural transformation has occurred be- ing concepts. A cycle of a graph is a collection tween to and ti, between t1 and t2, etc. We of lines of the form AlA2, A2A3, ... , An -1 An> illustrate this kind of graphical representa- and AnAl; the length of a cycle is the number tion with an anecdote: of lines in it. Thus each of the signed graphs A man M and his wife W were quarreling of Figure 1 consists of one cycle of length 3. (at time to in Figure 2) when a bystander B The sign of a cycle is the product of the signs intervened and tried to make peace (at ti) of its lines. Thus a cycle is positive if and whereupon man and wife stopped arguing if it has an even number of only negative and both turned on the bystander (at t2 ) . lines; the cycles of Figure la and lc are posi- We note that at to there is balance since the tive while those of Figures lb and Id are cycle of length 2 has both lines negative and The basic theorem bal- negative. concerning thus this cycle is positive. Then at t1 we find ance is the: a negative cycle of length 3 so that the struc- STRUCTURAL THEOREM FOR BALANCE ture is unbalanced and (in accordance with A signed graph is balanced if and only if its our empirical hypothesis) less stable. Finally points can be separated into two mutually at t2, balance has been attained by changing

FIGURE 2 171

FIGURE3 the structure. We shall now see several simi- was inclined to feel a disliking for B for this lar situation sequences among nations. and other reasons. Then E confiscated some important property belonging jointly to B and Toward Balance Tendency F (at tl ) . The result was that B and F in the Middle East attacked E, and I also attacked E. We use the following abbreviations in the President Eisenhower then expressed ex- diagrams presenting the dynamics of inter- plicit disapproval of these attacks. The next national relationships; and also in the accom- three figures are accompanied by the follow- panying discussion. ing three excerpts (respectively) from the E Egypt front page of the Ann Arbor News of Novem- A the other Arab countries ber 3, 1956. B Great Britain AMMAN, Jordan-( U.P. )-King Hussein of C Canada Jordan sent a warm message of thanks to Presi- F France dent Eisenhower for his support of &dquo;right and I Israel justice&dquo; in the Middle East conflict. D India CALCUTTA, India-( U.P. )-The United U U.S.A. States’ stand in the Middle East dispute today stirred an wave of pro-American- R U.S.S.R. unprecedented ism among the Indian press and public. H Hungary &dquo;Indian, American-bhai bhai [brothers],&dquo; The following developments are pictured was a commonly heard slogan. in 3. Some time B and F Figure ago (at to), USSR Woos , Blasts Britain, France were a toward both acting in friendly way E, MOSCOW-( AP )-The Soviet Union late which was quite hostile to I, which in turn today offered Syria &dquo;every assistance&dquo; and turned

FIGURE 4 172

FIGURE 5 heavy propaganda weapons on Britain, France the combined structure is presented in more and Israel. than three scenes. By Figure 8.0, 8.1, ... It appeared here the Soviet Campaign had two we mean 8 at time ... main targets: Figure to, tl, respec- 1) To destroy any remaining friendship Brit- tively. We restrict these figures to the eight ain and France have in the Middle East and Asia. points A, B, D, E, F, J, R, and U for relative 2) To divert the world’s attention from devel- simplicity. In Figure 8.0 we have the fairly opments in Hungary. static situation as it was before the recent The Hungarian situation, mentioned here events. en passant, will be the subject of a later section. This is a balanced configuration in which, in accordance with the Structural Theorem, In one sense, the three scenes of Figure 6 the two sets are I, are in incorrect chronological order and are disjoint given by Sl=(D, R} and At this both B better represented as in Figure 7. Here B S2={A, B, E, F, U). stage, and U were the of E and R are inimical at to, R builds up the posi- building up position tion of E at tl, and active hostility between with armaments and both direct and indirect B and E is induced at t2. economic assistance, which induced negative feelings from I to B and U. This situation, The Global Situation although balanced, was a strange one since it We now present the combined structure of found I in the same camp or coalition with which the previous figures are fragments or D and R not because of any explicit or im- substructures. Since the time instants to, tl, plicit friendship, but because they shared and t2 are different for these various figures, the same dislikes.

FIGURE 6 173

FIGURE 7

In Figure 8.1, the only change is the addi- Egypt’s nationalization of the Suez Canal ~ - in while the subse- tion of the positive lines RE and RA as is depicted Figure 8.2, realized in the form of bartering Czech and quent military attack on E by I and shortly with the in- Russian armaments for Egyptian cotton (with thereafter by B and F, together with the military advice included in the bargain). duced positive lines (in accordance shown in This has the effect of creating a situation Empirical Hypothesis) are Figure which is not balanced since (among others) 8.3. the cycles ERU and BER are negative. Both of these are balanced structures;

FIGURE 8.0 FIGURE 8.1

FIGURE 8.2 FIGURE 8.3 174

FIGURE 8.4 FIGURE 8.5 furthermore they have the same coalitions: Desires and Perceptions Sl={B, F, I, U) and S2={A, D, E, R}. The It seems clear that the balanced graph of main structural difference (not displayed Figure 8.3 represents fairly accurately the diagrammatically) is that the bonds have desires of R for a stable coalition. On the become more intense in the latter figure. It other hand the wishes of U would not be too is interesting to note that this situation, reflected in a balanced which although balanced, is not a pleasant one for badly graph U since the other coalition finds both R (with (from among the eight nations of Figures 8.0 its strong negative valence for U) and A,E through 8.5) has coalitions: Si==(R} and The somewhat (the controllers of an important commodity S2={A, B, D, E, F, I, U}. in U’s economy) together. Because of this unrealistic aspect of this possibility is that it fact, as well as the ethical and moral issues has I in the same coalition with A and E. involved in an unannounced attack on one However, this is precisely reflected in the weaker nation by two stronger ones, we have following quotation by former President in Figure 8.4 the American denunciation of Truman as reported in Drew Pearson’s col- the attack on E by B and F as well as by I. umn of January 5, 1957. This situation is not balanced since the I would make Israel the industrial country of cycles FRU and BDU are negative. In fact the Near East, then let the Arabs raise crops all the negative cycles of Figure 8.4 contain to feed Israel and themselves. They’re cousins. Ul The only change from this to Figure 8.5 They don’t have to fight. They’re all semitic is the vigorous reversal of sign from negative peoples. to positive of the directed line from D to U. It is clear that this approach involves the Thus the cycle BDU is now positive. How- difficult task of persuading both I and A to ever, as a result of the definite change in replace their strong negative bond by a sign of the line DU, the cycle DRU is now decisively positive one. From page 13 of the negative. A natural prediction is that the Hadassah Newsletter of November, 1956, considerable tension felt by the Indian gov- which certainly gives the Israeli viewpoint, ernment as a result of this negative cycle we can infer even from the headline alone DRU will cause D to consider a change in that the essential difficulty lies in the trans- sign in the line DR from positive to negative. formation of the sign of the directed line AI 175

FIGURE 9 FIGURE 10 from negative to positive, since I appears to CAIRO, Egypt-(AP) -President Nasser de- clared the United States and Soviet Rus- be ready for a positive IA line just as soon as today sia &dquo;were with us&dquo; when Egypt defended her- it can be arranged. self against British, French, and Israeli attacks. He denied his Arab allies had failed him. Israel Seeks Permanent Peace

The immediate results of Israel’s action were This is shown in the balanced structure the following: The imbalance of power in the of Figure 10, in which the coalitions are: Middle East, caused by the Soviet arming of Si=(B, F, I} and S2={A, E, R, U}. has been and the Egypt, corrected, consequent Another, perhaps even more striking dem- fear of an attack on Israel has been minimized. onstration, of differences in perception took Nasser’s ambitions for hegemony over the Arab I to world and the elimination of Israel received a place before B, F, and agreed withdraw set-back, perhaps permanently. Not only Israelis their troops. F or R proposed to U at that but many of the leaders of Arab states may now time that these two most powerful nations breathe easier. join in evicting B, F, and I by the use of their The last sentence of this quotation has superior military might. This proposal was other interesting implications pertaining to summarily rejected by U as &dquo;unthinkable.&dquo; the fact that some of the weaker Arab nations Figures 11 and 12 represent this situation as also felt threatened by the possibility of perceived by R and U respectively. In each Egyptian domination. of these figures, the proposal of R is made at time and the reaction of U is at Let us denote S=Syria, Q=Iraq, and J= ti given t2, Jordan. Then actually A=the Arab nations and in each of them a structural situation other than Egypt=(S, Q, J, ...}. With which was upset by the proposal of R was increased Soviet influence in Syria, there is restored. a balanced situation between Q, R, and S as The Situation shown within Figure 9 and as observable by Hungarian certain Syrian threats directed toward Iraq. We find in the Hungarian situation exam- Partly because of her willingness to continue ples of two different kinds of structural to accept financial support from Great Brit- changes. These are also amenable to analysis ain, Iraq is generally regarded as the most in the framework of structural balance. The westerly oriented of the Arab nations. This first is the strengthening of an already exist- is also displayed in the balance of Figure 9. ing bond without changing its sign. This is The perception of the situation by Egypt shown in Figure 13, in which two lines of the is nicely summarized in the following quota- same sign between the same pair of nations tion from the front page of a December, indicate a stronger bond than one line. Here 1956, issue of the Ann Arbor News: the developments involving the free world 176

FIGURE 12

FW=B, F, U, C, etc.; H=Hungary; and R= at t2 the official Indian government reacts to the U.S.S.R. are depicted. Each of the this suppression by condoning the act, but signed graphs of Figure 13 is balanced, but the people of India feel very differently and intuitively at t2, the situation is &dquo;most bal- criticize the U.S.S.R. for its actions and their anced.&dquo; Indian government for its stand in letters to The second kind involves the splitting of the editors of Indian newspapers and in other a point, in this case the point D=India, into well-publicized ways. The inevitable result two points, namely DG for the Indian gov- of this pressure of Indian public opinion is ernment and DP for the Indian people. At to realized at tg, when the Indian government we find (in Figure 14) India and the U.S.S.R. reluctantly makes an official anti-Soviet on friendly relations while the people of Hun- statement. When the two points DG and DP gary are making their try for freedom. This are then coalesced into the single point D, we attempt is forcefully suppressed at tl. Then obtain the balance graph at time t4. We note

Y FIGURE 13 177

for overt and covert acts, or for power as opposed to international sociometric choice or friendship. This problem calls for far more than a pictorial distinction which, of course, can be given by using lines of various colors. Namely, it is the operational inter- dependence of the various relationships which is important. 3. No distinction was made between durable underlying bonds and transient ones. For example, most observers would agree that regardless of the present status of the bond between B and U, it will ultimately revert to its previous traditional strong FIGURE 14 positivity. 4. The points used to represent nations that at time t2, the phenomenon of ambi- and groups of nations are themselves signed valence ( 3, 5 ) was in effect between DP and graphs. We have already seen two examples DG, with both a positive line and a negative of this phenomenon in microscopic view of line joining these two points. Here the posi- the point D in Figure 14, and that of A in tive line stands for the &dquo;unit&dquo; relation of own- Figure 9. This does not necessarily mean ership or identification while the negative that these two points decomposed or fell line gives the &dquo;sociometric&dquo; relation of apart, but only that they are examined more opinion on the like-dislike scale. closely. In terms of systems theory, we may ask how does the structure of its subsystems Limitations of the Theory affect the behavior of a system in its inter- We list here some of the conceptual prob- action with other systems? lems whose solutions would strengthen the theory of structural balance both generally The Prediction Problem and with regard to the kind of applications Even with the available theory, however, and representations discussed in this article. one can still attempt to predict from the pres- These show that we have indulged in con- ent situation, which is fairly represented in siderable over-simplification as a first approx- Figure 8.5. No one will argue that regardless imation. of what two coalitions (if any) emerge, U 1. We do not yet have a really useful will be in one and R will be in the other. model or accurate measurement of the degree There is also no doubt that B and F will be in of intensity of a bond between two points. the same coalition with U. There appears to One could denote by the numbers 1, %, 0, be more and more evidence that eventually, ~/2, and -1 the relations loving, liking, indif- D will choose to be in the same camp with ference, disliking, and hating respectively. U. The visit of King Saud to the U.S.A. is a But this merely provides a possible begin- clear demonstration of the intent of U to ning for the problem. break up the point A and carry as many of 2. In the graphical representation of the its components as possible into the coalition various events discussed here, there was no with U. distinction made between the lines standing With their present essentially dictatorial 178 controls, both E and S=Syria appear to be Their Vicissitudes," International Journal firmly in the coalition containing R. The of Psychoanalysis, 40 (1960), 287-90. 3. FREUD, S. "Instincts and Their Vicissi- only one of the eight in the six scenes points tudes," First published in Internationals of Figure 8 not yet mentioned is I=Israel. Zeitschrift für artztliche Psychoanalyse, Vol. This is a critical problem, and it takes more 3, 1915. Translation by C. M. BAINES in than a mathematical theory to achieve a per- Collected Papers, Vol. 4, Metapsychology, London: The 1925. manent peace. We shall not attempt to pre- Hogarth Press, 4. GUETZKOW, H. "Isolation and Collabora- dict on this point, other than to note that tion : a Partial Theory of Internation Rela- from all appearances, R has no desire to have tions," The Journal of Conflict Resolution, 1 I in its coalition. (1957), 48-68. The systematic structural balance approach 5. HARARY, F. "Structural Duality," Behav- ioral 2 255-65. of this article offers a clear approach to the Science, (1957), 6. —. "On the Measurement of Struc- of international situations. One can study tural Balance," Behavioral Science, 4 (1959), draw the signed graph of a given state of 316-23. events and examine it for balance. If it is 7. HARARY, F., and NORMAN, R. Z. Graph balanced there will be a tendency toward Theory as a Mathematical Model in Social Science. Ann Mich.: Institute for the status quo. If it is not balanced, one Arbor, Social 1953. should examine each of the bonds between Research, 8. HEIDER, F. "Attitudes and Cognitive Organ- the pairs of nations in a cycle with regard to ization," Journal of Psychology, 21 (1946), relative strength in the situation. One might 107-12. then predict that the weakest such bond will 9. MILLER, J. G. "Toward a General Theory change sign. for the Behavioral Sciences," American Psy- 513-31. REFERENCES chologist, 10 (1955), 10. MORISSETTE, J. O. "An Experimental Study 1. CARTWRIGHT, D., and HARARY, F. "Struc- of the Theory of Structural Balance," tural Balance: a Generalization of Heider’s Human Relations, 11 (1958), 239-54. Theory," Psychological Review, 63 (1956), 11. NEWCOMB, T. M. "An Approach to the 277-93. Study of Communicative Acts," Psychologi- 2. —. A Note on Freud’s "Instincts and cal Review, 60 (1953), 393-404.