Towards a theory of collective phenomena - Wiley Online Library

European Journal of Social Psychology, Vol. 21,49-74 (1991)

Towards a theory of collective phenomena: Consensus and attitude changes in groups

SERGE GALAM" and SERGE MOSCOVlClt *Departement de Recherches Physiques, T22 Universite Piene et Marie Curie, 75252 Paris Cedex 05 tEcole des Hautes Etudes en Sciences Sociales, Laboratoire de Psychologie Sociale, 44 rue de la Tour, 750 16 Paris, France

Abstract This study presents the outline of a model for collective phenomena. A symmetrybreaking model combines a number of well-established social psychology hypotheses with recent concepts of statisticalphysics. Specijically we start outfrom the regularities obtained in studies on the polarization of attitudes and decisions. From a strictly logical point of view, it is immediately clear that aggregation effectsmust be analysedseparately from group effects as such. The conceptual analysis of the assumed mechanisms reveals that when we deal with phenomena that have until now been designated as polarization phenomena, we are faced not with a single phenomenon, as was believed hitherto, but with a whole class of phenomena. For this reason it would be appropriate to deal with them diflerentially both from an empirical and from a theoretical point of view. It is possible to show, moreover, that in principle polarization is a direct function of interaction and, beyond a critical threshold an inversefunction of the differentiation between group members. A certain number of verifiable conjectures are presented on the basis of physio-mathematical-psychologicalconsiderations. It is to be hoped that these theoretical outlines will make it possible to give a new lease on Ife to afield of research that has established solid facts, but that became trapped in a dead-end road,for lack ofa suiciently broad analysis.

PRELIMINARY REMARKS The finest and most distinctive aspect of our sciences concerns the study of collective phenomena. Yet, in both social and natural sciences, this aspect is most difficult and certainly rather recent. W h e n facing this difficulty, the tendency is either to go back to the individual or to treat groups as collective individuals. Our purpose here is to carry further the study of these phenomena to fill the gap between individual and social descriptions. We will proceed combining established psychological concepts with those from contemporary statistical physics (Haken, 1977; Reif, 1965; 004627729 1/O 10049-26%13.00 0 1991 by John Wiley & Sons, Ltd.

Received 25 July 1989 Accepted 29 May 1990

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S. Galam and S. Moscovici

Stanley, 1971). A special effort will be made to explain how some complex sociopsychological facts emerge from other more elementary facts. It is well known that for about twenty years a large number of studies have been directly concerned with changes in attitude and decision-making groups themselves. Their most striking result was to find that consensus takes place around an extreme position, one which is close to the dominant pole of attitudes and norms of the population, and not around the average position, as was usually expected. This effect has been defined as group polarization (Moscovici and Zavalloni, 1969) in contrast to group averaging. Irrespective of conditions under which the situation has been reproduced and no matter what materials have been used, the effect has proved to be general and pronounced. Once this phenomenon was discovered, several theories were suggested to explain it (Doise and Moscovici, 1974; Myers and Lamm, 1976; Pruitt, 1971). The value of these theories is open to debate. However closer inspection shows that most of them fail to reduce the gap between attitudes and choices at the individual level (Burnstein and Vinokur, 1973) and decisions towards consensus at the group level (Davis, 1973; Davis et al., 1971). In this paper we will attempt to investigate various possible mechanisms whereby individual attitudes and choices are aggregated in the process of discussions and deliberations to eventually produce a common response. Using analytic methods developed in physics, (Galam, Gefen and Shapir, 1982; Galam, 1986) we will try to clarify the above questions to discriminate between mechanisms leading respectively to group polarization and to choice averaging. A better understanding of these mechanisms should motivate new experiments in laboratory to check our predictions which articulate around two main results whose consequences will be clarified later. On the one hand it is necessary to discriminate between aggregation effects and group effects which are related to specific interaction conditions. This implies to differentiate changes originating at the individual from those having a collective origin. This point is usually neglected ‘because group performance theories, generally, although not always, assume that individual-level changes lead to group-level changes (e.g. norm-value explanations of choice shifts; see Dion, Baron and Miller, 1970), an assumption not necessarily shared by theories that also allow for mere aggregation effects (e.g. Davis, 1973, 1982; Gelfand and Solomon, 1973). Moreover, empirical studies of group discussion often do not require group responses, apparently acting on an assumption of a simple individual-group relationship; for example studies of mockjurors have often drawn conclusions about juries, although no data were collected on actual mock jury decisions’(Davis, Stasson, Ono and Zimmerman, 1988, p. 919). This statement emphasizes with utmost clarity one of the most widespread biases of social psychology. On the other hand polarization is not a single phenomenon but a class of phenomena. In other words, consensus on a position or an extreme choice holds several meanings, depending on the process whereby it is reached. It is always very fruitful for a science to discover a class of effects where it was previously believed that there exists only one effect. If a theory’s heuristic value depends on its revealing conditions under which a phenomenon is produced and new effects are expected, then our theory meets all these requirements. It must be added that, for obvious reasons, the analytic tools and terminology available in social psychology do not allow us to explore these possibilities, at least not without great difficulties. For

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this reason the analytic method of statistical physics can be very helpful and moreover lead us to unexpected results, those mentioned earlier and others which will be discussed later. One further point, since this is the first paper in a series in which we hope to present a consistent and stimulating view of collective phenomena, we chose attitude change and consensus phenomena for practical reasons. Nowadays there is a proliferation of associations and committees set up to discuss and make decisions about research, health, the environment, ethics, and so on. This development is accelerating because neither traditional nor scientific criteria suffice to legitimize choices between the various alternatives that must be faced. The participants’ attitudes and values alone determine the consensus one way or the other. In short, there is a shift from common choices and changes of choices made by individuals to choices made by groups selected for that purpose. There is no doubt that social psychology has an interest in this problem and that it is expected to make a contribution which could help clarify what should be done in this respect. But there are also theoretical reasons for our choosing these phenomena. Polarization effects have been consistently checked on the basis of solid data. And yet the field of research dealing with them was shut down too soon and without obvious reasons. Perhaps this is due to both the lack of clarity on the analytic level and the lack of new prospects. We hope to open up the field again by presenting a set of conjectures whose psychological and social meaning will become apparent later and which will shed light on various aspects of a phenomenon which up to now has been reduced to a much too narrow point of view.

THE EMERGENCE OF CONSENSUS WITHIN AN AGGREGATE OF INDIVIDUALS

We often deal in social psychology with aggregation phenomena involving a large or small number of individuals. These phenomena are characterized by the fact that individuals who have no obvious relation to each other nevertheless behave in approximately the same way, either because they are identical or because they happen to be in an analogous situation (Alberoni, 1977). Fashion, advertising, or stock market speculation are striking illustrations of aggregation phenomena. On the one hand, people wear the same kind of clothes (jeans, short skirts, etc.) in terms of an identical class or generation and each person imitates or is imitated. On the other hand, people decide to buy or sell shares on the basis of agreed-upon indicators which vary from day to day without anyone knowing exactly in what direction. And this is actually a function of the diffuse opinion of all those speculating at the same time. ‘A conventional evaluation’, Keynes wrote, ‘which is established as the outcome of the mass psychology of a large number of ignorant individuals is liable to change violently as the result of a sudden fluctuation of opinion due to factors which do not really make much difference to the prospective yield; since there will be no strong roots of conviction to hold it steady. In abnormal times in particular, when the hypothesis of an indefinite continuance of the existing state of affairs is less plausible than usual even though there are no express grounds to anticipate a definite change, the market will be subject to waves of optimistic and pessimistic sentiment, which are unreasoning and yet in a sense legitimate where

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no solid basis exists for a reasonable calculation’ (Keynes, 1964, p. 154). Here we find individuals which behave in a certain way: they choose some look in dressing or get involved in stock market speculation, or they flee, in panic. One would not be justified in saying, however, that they constitute a social structure of which they are part and with which they identify. In short, they cannot be considered groups strictly speaking. Let us now examine the assumptions of our first model with respect to aggregation phenomena. In this model, an individual is represented by a discrete variable that can assume two values, c = + 1 and c = - 1. These values correspond respectively to a positive and a negative choice, a favourable and an unfavourable opinion, etc. Let us first consider a non-social state in which nobody is subjected to environmental pressure and nobody interacts with any other person. Under these conditions, it is normal to assume that an isolated individual will not aprioridiscriminate between a positive and a negative choice. It is just as likely that he will decide in favour of c = + 1 as of c = 1. This means that the two alternative choices are equally probable and hence exactly symmetrical. Let us further imagine a population of individuals characterized respectively by an indicator ranging from 1 to N. Each individual i can be associated with a favourable or unfavourable opinion or a positive or negative choice (Q = f 1) and so on. Since individuals are isolated from each other, they are assumed to choose independently and with equal probability between the two alternative response choices. If one of the individuals i is chosen at random, his choice will be ci = + 1, with a probability of 1/2, or q = - 1, with the same probability of 1/2. Under these conditions, it is obvious that the group’s collective choice that results from the addition of the N individual choices

-

N

c=cc: i-1

will on average be zero. And this average choice indicated by C = 0 represents a compromiseor averagingin contrast to the two extreme choices C = +Nand C = -N. The upshot of this is that even if each individual’s positions and choices change and no consensus state has the time to crystallize, the choice will neverthelessfluctuate around the average. In practice, this is not very likely, as individual changes of opinion are extremely rare (Davis et al., 1988). Therefore, in the absence of contacts and exchanges, a population of individuals would tend toward a compromise by making a common choice located exactly at the middle. Let us now consider a more complex case. It consists of two situations in which individuals are no longer isolated. In the first situation, the social environment applies an influence on each of them; in the second situation, they interact through discussions, exchanges of information, etc. (A) The first case can be associated to a coercive situation in which a pressure to conform and obey is applied. The coercion may involve respectively a majority, a leader, communication media, an institution, and a procedure. It is usually assumed that conformity pressure determines both the amount of risk one takes on in a group (Pruitt and Teger, 1967) and the direction of decisions (Turner, 1987; Mackie, 1986). We shall say that there the coercion of an external field Slays the groundwork for the outcome of the consensus with a probability that may be ver.?high. It applies a pressure on each individual to choose the positive or negative alternative, to the

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exclusion of the other. If S dictates for example a positive choice or a favourable opinion, the individual who is feeling its influence will either have to conform or set into conflict with it, that is, to deviate. To represent this well-known dilemma, we define the measure of individual conformity or conflict as the product Sq.It goes without saying that if Sci>O, there will be a tendency toward conformity and if Sci 0 will favour a positive individual opinion, while a field S c 0 will favour a negative option. This is what occurs, particularly, when we are dealing with a strong pressure, that of a leader, a dominant value or a powerful party. Consequently, the degree of interaction between a group of N isolated individuals and the external social field which applies a coercion on them is expressed by the quantity N

A=

Sc;

It can easily be seen that the amplitude of S measures the degree of conformity to be expected of each one. The question then arises what will be the form of the common choice. It is obvious that C=O is not possible any longer, as it was when individuals were not under pressure. Depending on whether the external social field applies a pressure towards the positive or the negative alternative, this choice can assume either of the two extreme values, C = N or C = - N. One and all flock to one or the other extreme, in principle, as they were ordered to do. On the whole, we observe a polarization, to the extent that the choice, the opinion around which consensus takes shape, coincides with the choice or the opinion that has been imposed. This could be expressed under the circumstances as a collective polarization, which results from the convergence of individuals in the direction of a position typical for the collectivity. In other words, the pressure to conform forbids compromise and replaces it by the alternative that was dominant from the very beginning. With these points in mind, one can outline three hypotheses in keeping with our formula: (a) Common choices may or may not be internalized by individuals at random, since there is no reason to assume that they underwent an authentic change. (b) Convergence towards an extreme consensus must take place quite rapidly once the direction in which pressure is exerted becomes known. (c) There is no direct connection between conformity pressure and the extent to which the group polarizes. It is reasonable to assume that even a minimal pressure emanating from the external social field will induce a maximal change (an extreme collective polarization) compared to the result that would occur if individuals were left free to choose or judge separately. This would imply that, contrary to a very widespread notion, a leader or a crowd do not need to be strong to induce individuals as a whole to take on extreme attitudes or to carry out excessive actions, as long as these individuals are separated and have little

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communication between them. This explains why authoritarian regimes view social mutism with such favour and why they find it advantageous to encourage, as recently happened in China, citizens to become informers on each other and thus isolated from one another for fear that their neighbours might denounce them. This might be a case where cause and effect are not proportional to each other. This non-proportionality is worth mentioning, since it was never taken into account in our theories and experiments as an important factor in decision-making, change, etc. within the group. In any case, it is apparent that there exists a connection between conformity and polarization, as has been argued previously (Cartwright, 1971) but in specific conditions which are defined by our model. These conditions lead however to a particular form of polarization, which we call collective polarization. (3)The second situation is characterized by interactions, exchanges, and contacts between individuals. It makes little difference whether they get into discussions, exchange information, try to persuade each other by judicious arguments, or communicate by gestures. The main thing is that they shed their isolation and hence exert a uniformity pressure on each other (Festinger, 1950), which is intended to prepare the ground for a consensus. Let us assume that this is the situation and let us take two individuals i and j who interact without experiencing any coercion from the external social field. What impact will their interaction have on the choice? We know that each individual has two choices, which result in the four following configurations: (a)ci= + i , c , = + 1 (b) C, = + 1, cJ= - 1 (c) ci= -I,c,= + 1 (d) C, = - 1' C.J = - 1 This set of configurations shows us that the two individuals can either converge by making the same choice or diverge by making different choices, that is, they may either reach an agreement or come into conflict. We shall describe their state by Icicj, where I > 0 measures the degree of interaction or exchange. It is obvious that configurations (a) and (d) both result in the same state of convergence I, while (b) and (c) result in - I, that is, conflicts. If we adhere to the first postulate, we will undoubtedly assume that the state of convergence will predominate, whether the choice is positive or negative. Here a symmetry arises on the level of coupled individuals and not, as above, on the level of isolated individuals. To measure the degree of convergence or divergence, that is, of agreement or conflict, we introduce the function

where (ij) refers to a sum of all the separate couples interacting (Ising, 1925). Let us now examine what will be the value of the common choice in a group defined by reciprocal actions of individuals not subject to any external coercion. We derive the formula C = fN when we apply the first postulate, as we did in the previous case. The only difference is that the interaction of individuals, in contrast to the interaction of an individual with an external social field, produces an extreme consensus whose direction is completely arbitrary. For the positive or negative choice

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has the same 112 probability of occurring. However, on the whole, it will in fact be one or the other, + N or -N but not both. We are faced here with a very pronounced spontaneous break in symmetry with respect to individual choices, though collective choices remain equivalent. But from the point of view of social psychology the crucial fact is the following. The multitude of contacts, exchanges, and discussions in the population, as occurs with rumours or deliberations, will in the final analysis lead to an extreme consensus. What it does not necessarily determine at once is the positive or negative direction of the opinion or choice that will prevail. It may be assumed that this is what happens in groups of individuals whose volatility indicates that they will act in an excessive way. It remains true, nevertheless, as has often been asserted, that it is impossible at the start to predict whether the outcome will be an enthusiastic or hostile, a violent or a panicky reaction. And in most instances, groups will oscillate from one to the other extreme. For several uncontrollable causes intervene to lead to the actual result. To keep to a more familiar area, however, it follows that individual interactions are likely to induce what might be called an inter-individual polarization, an extreme choice whose direction is arbitrary. We are dealing here with an extremism in the common sense of the word, which depends more on the antecedents, the force of the arguments, than on whatever dominant values might exist. The main hypothesis that can be deduced from it, in any case, is that the degree of interindividual polarization is a positive function of the degree of interaction. It must be kept in mind, however, that social and psychological factors of various kinds (organization, amount of information, etc.) restrict the direct character of this function. This has been shown in various studies (Moscovici, Doise, Dulong, 1972; Moscovici and Lecuyer, 1972; Forgas, 1977), although the question has not been satisfactorily clarified. In short, we have seen that isolated individuals can coordinate their choices and reach a consensus which is a compromise between their opinions or choices. This consensus can result from several configurations of individual opinions or choices which change so as to compensate each other. Consequently the apparent group stability may have as its counterpart incessant change and reversals in the decisions of those who participate in it. And yet, symmetry and equal probability prevail all along between the alternatives envisaged. This symmetry is disrupted as soon as an external social field which applies a conformity pressure on all individuals manifests itself. The same thing may happen when strong inter-individual interactions occur, with each individual acting as an external field with respect to the other. In both cases, individuals converge towards extreme opinions or choices. And chances for a compromise consensus generally considered to be a reasonable ideal will diminish in both situations. A difference remains, nevertheless, between these two cases: the conformity pressure moves the direction of the consensus toward the dominant pole, whereas the intensity of interactions does not allow any specific direction to be predicted. In one case, we have a predetermined collective polarization, in the other, an interindividual polarization that is reached as the discussion progresses. It is quite clear that when one compares the various ways in which groups reach agreement in social psychology, one must take into account what is the predominant position when changes in attitude, choice, etc. take place. Those who assert that conformity constitutes an indispensable element carry things too far, just as do those who by denying

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any role to interactions (Vinokur, 1971) are over-simplifying reality. We now know why. It is because they are unable to make a fine distinction between the conditions in which individuals are led to move towards a dominant pole and those involving an extreme reaction, which occurs in an arbitrary way depending on the cycle of group exchanges hic et nunc. Let us now try to determine what happens when the coercion of the social setting and interactions between individuals occurjointly. This is a mixed aggregation set-up, like that of a crowd identifying itself with a leader (Moscovici, 1985), a collectivity whose members have a predominant identity or which must act in line with a model imposed from the outside. To gain a good perspective on the events, let us visualize a group of N individuals q, who are kept together by pressures from the external field S and who interact in pairs. We can introduce a function G which, for a given configuration of choices ci, measures the degree of convergence, agreement or divergence, or even of conflict, in the group, G = A E, which becomes:

+

N

(4)

There is little risk in stating that, according to the first conformity postulate, each individual will be strongly in the direction of S. In this case, the expression G can be rewritten as follows

or

IN

G({ci)=-lifS>O) = 2 e -

NS

with a single configuration of individual choices. Here e represents the number of persons in the group with whom each individual interacts. If this analysis is correct, individuals may be said to be depersonalized (Turner, 1987) and assimilated to the crowd, the group. Literally speaking, they are considered nonexistent, irrespective of how they interact. Collective polarization therefore does not exclude interaction as such, but it does remove its individual character. This perspective reverts to a point of view expressed by mass psychology, according to which the obliteration of personal differences is responsible for the extreme volatility and excessive opinion of crowds. But this is too broad a subject to be treated so offhandedly.

CONSENSUS AND TRANSFORMATION OF INDIVIDUALS INTO GROUPS

So far we have looked at the repercussion of aggregation phenomena on common opinions and choices. Let us now turn to group phenomena as such, that is, phenomena where actions and relations between individuals are determined by social representations, norms that everyone must share if he wishes to participate in exchanges with others. Both representations and norms make themselves felt through the educa-

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tional process and lifestyles which shape most people’s psychological type. Every choice and every opinion is thus shaped by a scale of values to which people subscribe affectively and intellectually. These values, which are inculcated in the group, in practice introduce an asymmetry with respect to the importance attributed to information and arguments and with respect to the meaning discussions take on when a consensus is sought. This consensus is in some way prepared and biased by this common fund of values individuals uphold, at times even unconsciously. Junes for example should consider the ‘guilty’ and ‘not guilty’ alternatives of a verdict on an equal footing. In fact the values of our contemporary society incline rather toward clemency. As a result, several experiments with fictitious juries show that majorities whose verdict is ‘guilty’ are less common than those in which the majorities reach a ‘non guilty’ verdict. The clemency bias seems to be due to a norm that protects the accused, according to which it is better to acquit a guilty person than to condemn an innocent one (MacCoun and Kerr, 1988). This means that majority pressure is not responsible for the conformity effects attributed to it. The probability that it enforces its verdict depends on the agreement or disagreement with the values shared by the members of the group. In other words, these values produce an asymmetry in the consensus which is so often emphasized by moral philosophers. In the third case, we are attempting to convey the idea that each person, in his capacity as a group member, is a priori bound to a certain choice or attitude by common representations and norms. For this reason it is difficult, if not impossible, to reverse these choices, these attitudes, without facing the risk of cutting oneself off from the group with which one is associated and of suffering personal anguish. Let us now introduce the concept of an internal social field to convey all that is inculcated to us by the culture in which we live. This internal social field leads individuals to be ‘personally’ inclined to opt, for example, for a positive rather than a negative alternative, clemency rather than culpability. This internal social field, like the external social field, disrupts the symmetry of personal choice or attitudes. The difference is that the internal social field manifests itself separately within each individual and may even vary from one individual to the next. We are dealing, in effect, with a local and differentiated field, whereas the external social field is encompassingand uniform for all members of the population. The following formula expresses all these relationships

v = c S.C. N

i-I

I

1

(7)

where, as we have just explained, Simay vary in sign and intensity from one group member to the next. To quantify Siwe must treat it either as a probability function with a distribution of Si,p{Si},or else know the configuration of the {Si}. But to solve this function specifically, we can reformulate the first postulate in a way which plays a large role in several theories, particularly Sherifs (1936). The theory states that, in the absence of an external social$eld, individuals tend to interact with each other and behave in Iine with their internal socialfield. The more uncertain and vague the former, the more strongly the latter determines each one’s behaviours and judgments. In one word, intersubjective reality replaces an objective reality that fails to offer support. This explains why, in line with this expression of the first

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S. Galam and S. Moscovici

+

postulate, if Si >0, the individual chooses ci= 1, and if Si< 0, the individual chooses q = - 1. It follows from this that the consensus on the common choice of group C is now exactly equal to the average of Si normalized within the group, that is, it is equal to the function

In this case, C = B, which means a compromise. From a formal point of view, something new has been introduced compared to what we saw previously. The novelty lies in the fact that from here on out, C can vary from C = N to C = -N,including C = 0. What we now have is a sort of continuum in the range of choices on which the group might agree, going from one extreme to the other and including averaging, without thereby modifying its nature. This is in keeping with the consequences of Sherifs theory, which he tried to verify by his classic experiments on the autokinetic phenomenon. However, if we look at it more closely, we can see that what we have is one constellation among four possible constellations, all of which are of definite interest to social psychology. The first two are derived from equation 7. (1) All individuals have been shaped by the same mould, they have internalized the same values and therefore have an identical social field. In that case, we have an internal conformity that is equivalent to what external conformity would be under the pressure of an external social field. To test it, one needs only write p(S) = d(S,- S) and the same situation will arise. (2) Values with opposite signs, positive and negative, favourable and unfavourable, are equally frequent. In other words, we have partition, two sub-groups that each adopt opposite values (Burnstein and Vinokur, 1973) during their discussions in preparation of a consensus. This amounts to stating that the Si fields are distributed with an equal probability between S and -S.On the basis of the expressionp(S.)= ‘h[6(Sl-S)+6(Si +,$‘)I, a compromise again emerges. And it corresponds to the &ation where group members think or decide by themselves in the group, without the group’s applying any coercion on them. In truth their behaviour could be designated as selfish or individualist. (3) The third case corresponds to the presence of equations 2 and 7, that is, when both an external field S and internal fields Si simultaneously intervene. The external frame of reference and the internal frame of reference, values, in effect, exert contradictory influences on the group members. It is in these situations that we often observed the group majority trying to impose its point of view on the minority and asking its members to carry out actions contrary to the norms which had been inculcated in them, doing the opposite of what they said, and so on. Whenever an isolated individual (that is, Z = 0) is trapped between the external pressures of field S and the internal pressure of field Si,he will go along with the stronger pressure when the signs are opposite. He will then experienceeither a conflict with the majority because of his loyalty to traditions and norms that he has accepted, or an internal conflict, arising from the execution of an action that he condemns. On the one hand we have a deviance conflict, in the other, an obedience conflict, both of them quite common.

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(4) The last case occurs in the presence of equations 3 and 7. This involves situations in which there are interpersonal divergences and oppositions, where two neighbouring individuals i and j have antagonistic fields Si and Sjand must nevertheless reach an agreement on a single position. Where S=O, if their link I is strong compared to Si and Sj,they will not have any conflict between them, but one of the two will experience an internal conflict to the extent that the choice of (i) and of ti) will go along with an Sior an Sjthat wins out. In practice, these four constellations spell out a statistical description derived from expressions 2, 3 and 7, which led to the general expression for the degree of convergence of the group N N

G { c i , S i } = I C C.C. + S C c . + C S c , y

’J

is[

i=1

(9)

where the data for Sior p(Si)is given. We now turn to a more dynamical aspect. Let us consider a group of individuals each having his own local field Si,an inclination toward one or the other alternative determined by the value by which he has been affected. Let us thus assume that for instance 65 per cent of them are inclined to be pacifists and 35 per cent nonpacifists. If there is no discussion or interaction between them, one would presume that their common opinion about the need for disarmament negotiations would be determined by the difference between the two percentages. Let us now put them in a situation where they must agree on a common position after having debated, exchanged arguments, as we usually do in ourexperiments. It is reasonable to consider these debates, exchanges, arguments, etc. as creating a sort of virtual field, a participation field similar to the field of forces described by Lewin (1943), which exerts an internal pressure on the group members to converge toward each other. On the basis of the previous formulas, we can describe this participation field as follows: el C S,=----2 ( N - 1)

where interactions of each individual are limited to a number e of individuals in the group (see Appendix 1 for derivation of equation 10). The presence of C shows us that this virtual field is a function of the possible value of the group’s common choice, a value that would be near the dominant pole of the scale. The deliberations of a fictitious jury, for instance, are a function of the tendency toward clemency which shifts the consensus in the direction of the not-guilty verdict favoured by the majority (Davis et al., 1988). By introducing the participation field into expression 9, the latter becomes (see Appendix 1)

” + S + S.)C.

G ( c i }= - S v r + C(S in1

”

1

1

The matter does not end there. Let us see what happens, in principle, at the level of group members. It is reasonable to assume that the field created by discussion between the participants results in their becoming more involved. In the process, each participant’s internal social field is modified and shifted in the direction of what becomes the explicit group norm. This is exactly what often happens during discussions, when the participants become aware of values that underlie their choice

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and hence attribute greater influence to them (Janis, 1972). The effect of these exchanges is expressed by the field SiRresulting in individual involvement, which is the sum of the virtual participation field, the internal or local social field and, possibly, the external social field, inasmuch as there is always some conformity pressure. Under these conditions, equation 11 can be expressed in a form equivalent to 7, which is

where

S R = S+ s + s

(13)

This is a way of describing a process initiated by individuals each with his own internal social field Sj, which is constituted by norms and representations that he accepts and considers legitimate. By participating in group discussions and feeling involved by whatever consensus is finally reached, the individual changes by internalizing a new norm or representation, whichever one was reinforced during the discussions and exchanges of arguments with his fellow-members and which is expressed This is what we observed and measure by the post-consensus test, in which by SiR. the group members, after the end of the discussion, are alone once more when they express their views. We assert that this internalization is a necessary and specific consequence of the group process and distinguishes it from the process that takes place when there is a mere aggregation of individuals. Thus, what most theories, with the exception of the involvement theory (Moscovici and Zavalloni, 1969), apprehend as an empirical fact, is derived here from the concept of an internal social field and especially of a field resulting from the participation of the group members, namely field SIR. We believe, to be sure, that during discussion and information exchanges whose function is to reach a consensus, each member ci wants C, the common choice of formula 11, to be as large as possible. This means that each individual favours an extreme consensus, as both social psychology and physics require, in order to maximize its compatibility with the virtual field S, as well as to harmonize with the values to which he subscribes ardently. In which direction will the individual tend toward the extreme? Since S, and C, according to 11, are in the same direction, this extreme choice will be the one closest to one of the two poles of the scale of attitudes or choice, pacifism, a clemency verdict, and so on. As was true of the two cases previously described, the result will therefore be an agreement on a common choice, C = i l v , that will lie at one extreme. But which extreme will depend on the internal social fields, the dominant values among the group members, according to whether they tend toward + N or -N,and by no means exclusively on the external social field or on interactions between the group members. In other words, participation in exchanges and discussion results above all in the reinforcement of attitudes or decisions in the direction that originally prevailed in the group. Once consensus has been obtained with respect to an attitude or common decision, the latter brings about a change in each individual in that it becomes his very own. In the last analysis, the result is what we consider a genuine group polarization. One might say that through the interaction that takes place between autonomous and equal individuals, the group obtains what can only be obtained by conformity for a mass or an aggregation, when individuals are put in an unequal and dependent

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position. And the group obtains it to the extent that the interaction becomes more than a means of simply exchanging informations or opinions between the group members and serves as an end in itself. It embodies the members’ desire to participate in order to make joint choices or to take joint stands. Instead of leading to decisions and attitudes with an arbitrary meaning, these exchanges and interactions lead to a meaning that reinforces the norms and representations that link the individuals to each other and to the group. This alone is enough to discriminate the participation process which leads to group polarization from the coercion process or the exerting of authority which leads to a collective polarization. It also suffices to discriminate the participation process from the process in which there is an exchange of information or an interaction leading to inter-individual polarization. But all three processes together constitute a class of similar phenomena characterized by the shift in consensus towards one of the extreme positions on the scale ofjudgments, attitudes, or decisions that has been noted with astonishing regularity in our science. These equations make it extremely easy to see that if individuals maintain the same position, a priori, on the choice they will make, the group is incapable of reaching an agreement. Neither discussion nor majority pressure can induce a change in the norms or representations of the participants. In the language that we have been using here, this means that the internal social field of each member is stronger than the virtual field arising in the course of the interactions. In other words, Si and SiRhave the same sign for each individual. Group participation has not modified anyone’s attitudes or positions. Surely, we know that, in general, the firmer the group members’ convictions, the more vigorous will be the discussions and exchanges of arguments (Paicheler, 1976). But beyond that, one must take into account the theoretical proposition that there is an implicit relation between the strength of interactions and the strength of each person’s values, as seen from the degree of certainty or commitment. And a consensus can be reached to the extent that the forces of interaction are stronger than the forces of each person’s own values. It is difficult at present to measure these forces in order to formulate propositions that are more than qualitative. There is nothing that prevents one from thinking, however, that one day the means for doing so will be forthcoming. At that point, it will be possible to put one of the deductions of our model to the test, and the results will have great practical significance. CONSENSUS PARAMETERS

Building our model around the idea of symmetry breaking, we treated various phenomena which result from respectively mere presence of individuals, aggregation process, and groups facing a choice. It appeared quite naturally that a choice made by isolated individuals leads to compromise, whereas this choice leads to polarization when made by an aggregate of individuals or a group. These are fundamental orientations. Carrying out the analysis one step further, we deduced from this idea that the three mechanisms -conformity, interaction, participation -lead to specific forms of polarization which are characteristic of each one of them. Where it was believed, that a single effect was involved, it now turns out that there exists a class

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of effects which can be described very accurately. We did not expect this result when we initiated this investigation, but once the result was obtained, it seemed natural and consistent with known experiments. It is thus clear that the field of investigation is broadened when physics is not used only to produce images and terminology but rather to generate hypotheses for social psychology. At this stage to formulate these hypotheses, some of which havejust been suggested, the model must be completed by discussing the parameters involved in collective phenomena we are dealing with. In order to make the model applicable to reality, we will discuss the following four fundamental parameters: differences in choice, degree of interaction, number of individuals, and decision rules. It is out of the scope of present work to analyse each one exhaustively. We will concentrate primarily on main principles. It is known that consensus tends to bring individuals closer together and so to speak ‘line them up’ with one another. Consensus presupposes a shift in the direction of convergence which both decreases discrepancies between people’s views and reduces conflicts during exchanges which construct the desired outcome. Up to this point, we have assumed that the group, on the whole, aims to maximize this convergence of attitudes and choices in order to reach a common position. But we know that this assumption is only partially true. Actually, in many circumstances, and especially where change is needed, the contrary is true: tensions and divergence movements are favoured. Rather than pushing to assimilate individuals to one another, the aim is to emphasize those features which differentiate them from each other. By highlighting these differences, it is hoped that each person’s particular abilities will be stimulated to the benefit of the group as a whole. This kind of evolution can be observed today in the socialist countries. Having for many years done everything possible to preserve the trappings of obedience and conformity in order to guarantee a unanimous consensus, they now are trying to go into reverse to encourage both differences in expressed opinion and individual participation. Societiesand firms seek to reach a similar goal by a variety of methods. It is interesting to note that the stability of social systems and the capacity to change so as to adapt to modern requirements depend to such an extent on their capacity to arouse divergences, on non-conformity of opinions about the choices to be made in common. It has become the better part of wisdom to provide space for the institutionalization of dissidence. To spell out these remarks formally, let us introduce a ‘divergence’ parameter D into our model. It means that the group can recognize one individual, or two, or three and so on, who are divergent. For instance, in the case of one divergent individual, an internal dynamics takes shape due to the fact that anyone of the N group members can be the one who deviates. Instead of having a single configuration associated with the extreme choice * N , we have instead Nconfigurations. The upshot is that the group has a larger set of alternatives in reserve. This surely is an incentive for individuals to change their position independently, even though the common overall position is not necessarily modified thereby. This explains in part, as we mentioned earlier, how a group may remain stable while allowing individuals to diverge and letting conflicts proliferate. To control the effect of D on internal dynamics, we introduce the function richness of alternatives as: R = D log W(C)

(14)

Theory of collectivephenomena

63

where W(Cj is the number of individual choice configurations associated with the .agreement on some common choice C.Let us point out that R corresponds to entropy in statistical physics, with D playing the role of temperature (Reif, 1965) in the appropriate unit. By ascribing an instrumental meaning to the possibility of divergence, we have therefore tacitly suggested a second postulate, i.e. that the group always tries to increase its stock of alternatives, R, as various means of coping with the variability of reality. Is this a justifiable hypothesis? Upon reflection, it is justifiable to a certain extent, if one allows for the division of labour, the multiplicity of sciences and arts, the variety of institutions on which a changing society relies. The group unquestionably also imposes some limits, however, either by trying to slow down the pace of divergences or by eliminating the alternatives that are at odds with its current goals. We have now reached the point where we can join together the effects of the first postulate, which encourages convergence at the level of individuals with those of the second postulate, which encourages divergences or even conflicts at the group level. As was just shown, for a common choice C,a number W(C) of individual choice configurations leading to C can be considered. But these configurations are bounded with a degree of convergence and divergence that must now be estimated. For this purpose, all that needs to be done is to calculate the aGerage value of G(Ci) (equation 9) over the range of configurations W(C), ( G ) , . It is highly likely that the group will attempt to narrow down this range so that the growing stock of alternatives does not prevent a certain uniformity among persons forming the group. It seems reasonable to us that the pursuit of personal distinctiveness, in fashion, for instance, goes hand in hand with mass production, that originality is complemented by imitation, just as a musical theme is recognizable even in the form of variations. The same holds true for science: discoveries are encouraged and given priority. Notwithstanding, most routine efforts are encouraged, because they reflect professional competence. This is a valid enough reason to publish them, though in many cases they will rarely be quoted. Overall, the group acts as though it were governed by a third postulate, which requires to optimize the two opposing effects of innovation and conformity by maximizing its power with respect to the outside world. That is, to control the setting in which individuals operate. We define this power in terms of the following function: P=DlOg W(C)+ ( G ( c ~ } ) ,

(15)

If we look at this function, we recognize that the group will select the common choice which maximizes P, that is, so that

6 P = Oand,-d2P < 0 6C

sc

Power thus appears necessary to harmonize the two trends which determine the aggregation of individuals into a group. It is unfortunate that social psychology did not look at it from this angle. Moreover power was not investigated in depth, and also we have failed to grasp its role as controller of the two tendencies, which, if left unchecked, would end up by mutual annihilation. It is, all in ail, a very delicate task to delineate what are the respective scopes of external coercion and interpersonal exchanges, if as well their fusion as their dissociation is to be avoided. That is,

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it is difficult to avoid reducing divergences to almost nothing or else increasing them without setting a limit, when no power exists to restore them to a moderate level. We do not wish to dwell on this point now, because it would add too much complexity to the physical and mathematical analysis. But we will return to it at a later point, in view of its interest and of the prospects opened up by such a viewpoint. It should be noted that equation 1 1 represents quantity { G(ci} ) ~. To obtain it, we have identified individuals cj who are neighbours of ci in terms of the value of the colicctive choice for a group of (N-1) individuals, divided by (N-I), (Appendix 1, equation 1.3). If for ci we substitute CIN in equation 12, we obtain el

+ CS + CS,

{G{c~}),=-----(C~-N) 2(N- 1)

Let us now be more explicit in order to delve more deeply into our model. We have a group of N persons ci who are in a position to make decisions, either for choice + 1 or choice - 1. There is a given divergence parameter D. The problem is to determine which value of the common choice, C, maximize the power P of the group. Or, to put it differently, given the divergences that exist between the members of the group, what must be the agreement point that will strengthen the latter's control over the former in such a way that the inherent conflicts do not lead to the break-up of the group. Let us say that N , and N- represent the respective number of individuals who chose 1 and - 1. We have

+

N = N++Nand To obtain this common choice, we first calculate the number of configurations from N! W(Q=N,!N_!

(19)

By using equations 17 and 19, we obtain an expression for the power function: ( N + C ) ! ( N - C)!

P(Si)=-e2 (N-1)

The solution of dP/dC=O, after an average over the {SJ, gives the value of the common choice as a self-consistent equation, namely (see Appendix 2)

5 =/dSiP(S,)th [( N

elN D(N-1)

-1

+ -)1 C +S + Si

NN D D

This fundamental equation can be analysed in the simplest case, where there is neither an external nor an internal social field. When both S and Si are equal to zero, equation 21 becomes

+qa}

a = # D(N- 1) N

where a represents the common choice C/N. The question now arises under what conditions there are zero, one, or several solutions for a. To answer this question,

Theory of collectivephenomena

65

we can solve equation 22 graphically. We inscribe the two equations y = a and y = th (aa) on the same graph, as a function of variable Q where eIN

1

a= D ( N - ~ ) + N

The curve y = a is a straight line going through the origin 0,= a = 0) with a slope

I

-0 I

I I

y = q

,'/ I

Figure 1

equal to 1. Curve y = th (aa) is more complicated. It too goes through the origin, but with a slope tangent equals to a. When la1 is very large, it tends toward two asymptotes, y = 1 and y = 1. The solution or solutions for a in equation 22 are obtained at the intersections of the two curves y = a and y = th(aa) on Figure 1. We can see that a = 0 is always a solution. On the other hand, the two symmetrical solutions, a. and -ao exist only if a > 1, hence the condition

-

D