Dynamics of Conformity and Association

In the previous sections I’ve made some speculative predictions, both at the level of the individual or dyad and also at the level of groups, about the dynamics of information which is socially transmitted. One thing which has become apparent to me as I become more familiar with decentralized systems and emergent behavior is that it is extremely difficult to guess what the system’s global performance will be, even when the rules of the components are fully understood. It might seem that many of the statements I’ve made about the properties of social networks and information transmission imply dynamics which would lead simply to a general homogenous mixtures of transmitted culture. Yet there are many real-life experiences of social structure and transmission where this is not the case. How could simple transmission rules create complex patterns? What are the potential impacts of cultural transmission for the creation and modification of social groups? What classes of processes might drive group formation and dissolution, and how does the presence of groups in social structure affect transmission and population-level properties?

A recurring result of research into the behavior of systems is that even simplistic problems which have intuitive results become much more complex when the problem is spatialized. What I mean is that when notions of space, time, and distance are explicitly coded into the rules governing the operation of a system, it may show behavior which is radically different than when assumptions of homogenous random mixing or instantaneous effects are made.

An example of this are the Lotka-Volterra based models of predator-prey relationships in which the size of one reproducing population (the “foxes”) is dependent upon the size of another (the “rabbits”). Because the foxes only eat rabbits, if the number of foxes were to increase beyond a certain point, there wouldn’t be enough rabbits to feed all of them and the “extra” foxes would die. In the most simplistic case, the numbers of foxes and rabbits in the system would change until they achieve a balance, and this equilibrium point would be dependent on their relative rates of reproduction. However, if the model is made more realistic by allowing factors like a time lag between the birth of extra foxes and their eventual death due to starvation, the relationship between the two populations becomes much more complex. The extra foxes may kill off too many rabbits, eventually causing the fox population to dive below its equilibrium level because not enough rabbits can be found. The rabbit population can then increase because there aren’t as many foxes eating them. Once the rabbit population increases, the fox population may as well. Depending on the parameters, the populations in the system will crash to extinction, get locked into alternating cycles, or in some cases, jump around chaotically. (Bar-Yam, 1992, p. 586) This example exhibits complex behavior in time, there are corresponding effects in the spatial realm.

The near indistinguishability of cause and effect seems to be one of the essential complications for any analysis of social systems. Social structure is generated by the interaction of individuals but at the same time it guides their interactions. In essence, each step in time takes as its input the output of the previous step. This non-linearity, or dependence on previous states, is usually one of the prerequisites for the interesting classes of behavior exhibited by complex systems. Non-linear systems often have the potential to drift into either chaotic or well ordered states, depending on the initial conditions and driving parameters. This might mean that any chance occurrences of structure in the initial conditions of a system could be drastically emphasized through iterative processes: effects which are seemingly insignificant on the level of individuals could be drastically amplified at the population level. The opposite could also be true – the structure of the systems might be such that the starting conditions do not matter; the system will always progress to an “attractor” of a certain set of states. My point is that models of social process, and the tools for their analysis, need to explicitly consider these sorts of complex, time-based interrelationships. Contemporary theory is getting better about this, but is easy to slip back into a pattern of thinking of external causes directly producing observable effects.

Ole-Jorgen Skog (1986) presents a fascinating analysis of population level trends in alcohol consumption data in Norway. (Figure 15) The data show interesting periodicities, but frequency analysis shows that the time series is qualitatively similar to one which could be produced by a random walk.

Thus we may conclude…that very long waves of alcohol consumption exist, but [the analysis] does not necessarily support the idea that these waves are the result of systematic and long-term processes with a persistent direction. The results obtained in the time domain could even be taken to suggest that something resembling a random mechanism is at work. (Skog, 1986, p. 12)

Fig. 15 Graph shows alcohol consumption per capita 15 years and older in Norway 1851-1982. Prohibition in Norway lasted from 1916 to 1927. (copied without permission from Skog 1986 p.6)

He then presents arguments suggesting that if an individual’s alcohol consumption is related to the consumption of her peers, the structure of the social network might be such that there is some degree of “coupling” of individuals’ choices at the group level: “I have argued that long-range indirect ties may create sufficient integration in very large populations to produce a breakdown in the law of large numbers.” (Skog, 1986, p. 29) In other words, if the social effects of drinking culture are strong enough, individuals may not be independently making their choices about how much to drink. Social groups may tend towards internal homogeneity, “choosing” as a whole at each time step, rather than averaging out individual’s choices.

Skog’s analytical results are important because they show that it is at least hypothetically possible for the coupling of individual choice and social structure to drive a cultural parameter to values which are not what would be expected if each individual acted according to some internal preference model. The problem is analogous to one in the US system of electoral voting: due to the discrete nature of a State’s choice in the electoral college, a candidate can lose in the popular vote and still win the election. Skog is arguing that the implicit rules of culture may create the same kinds of paradoxes as the formal rules of an electoral system do. Also, the actual dynamics of cultural phenomena may be more dependent on previous states of the system and interaction strength than on some of the presumed economic or legislative driving parameters. Although observed per capita alcohol consumption is certainly not totally historically independent, prohibition does put a big notch in the curve.

But how strong are the “internal homogenization” effects? Joan Rentsch (1990) published an interesting study of interaction and changes in organizational meanings in an accounting firm. She used interviews to collect lists of events and polar terms used to refer to them. The employees then took a survey which asked them to rate the meaning of various organizational events according to the polar terms. She also collected self report interaction data so that subgroups could be identified by using social network analysis. The hypothesis was that the service staff of the accounting firm in the study interact with each other more than with the heads of the firm, so the staff may interpret events in ways similar to each other, but quite different from the conception of events held by other “higher up” groups: “The results provide evidence that people who interacted with each other had similar interpretations of organizational events and that members of different interaction groups attached qualitatively different meanings to similar organizational events.” (Rentsch, 1990, p. 268) As in every study of this kind, the actual causality must be inferred. Perhaps the formation of groups with similar view points is a result of people’s preference for people similar to themselves, rather than solely a result of the interaction. Probably both processes are in effect.

Interactions which lead to increasing similarity among the participants would not necessarily lead to loss of diversity at the system level. Axelrod (1997) has written a compelling paper on a simulation in which agents were located on a spatial lattice and exchanged portions of their “culture string” with their neighbors. The simulation was set up so that the probability of exchange was greater for agents whose strings were already similar.

Fig. 16 Each map shows “cultural similarity” between cells in Axelrod’s simulation at different points in time. Similarity of the culture strings in adjacent sites is coded as: Black < 20%, Dark Gray = 40%, Gray = 60%, Light Gray = 80%, White = 100%. This run was conducted using five cultural features and ten traits per feature. Each site has for neighbors. (copied without permission from Axelrod, 1997)

Runs of the simulation generally resulted in the emergence of a structured pattern of associations between agents (Figure 16). The distribution of the attributes held by the agents on the spatial grid showed a large degree of “patchiness”. It seems reasonable to assume that the same kind of phenomena might occur in real human groups. However, the model has not been investigated in depth to determine which structural properties are necessary. It is likely that it would require some sort of discrete trait (or discrete informational unit), as well as preferential association based on detectable possession of traits.

Kathleen Carley (1991) presents a related model in which agents are not restricted to interaction with their immediate neighbors, but are members of a fully connected group social network. She tracked the existence of groups (measured as collections of agents with mutual interaction probabilities greater than their probabilities of interactions with the rest of the population) as the agents exchanged information with interaction probabilities weighted on the basis of the number of “facts” in common. In contrast with Axelrod’s model, all of Carley’s simulations eventually converged on mutual interaction and a homogenous distribution of facts. (Fig. 17) However, the time to convergence and the dynamics were strongly effected by the relative sizes of majority and minority groups, initial network conditions, and proportions of shared knowledge.

Fig. 17 Sample run from Carley’s simulation of group stability. Plot shows relationship between Intergroup and Intragroup interaction probabilities over time for one group in a two-group society. (copied without permission form Carley, 1991, p.343)

Clearly the specifics of the design of the models are very important. Carley was mostly interested in the dynamics of a very small population – her largest group was 12 individuals. It would have been fascinating if Carley had run a simulation on a social network which was analogous to Axelrod’s lattice. In one sense, the difference in results between the Axelrod and Carley models is encouraging. The formation of groups and subcultures in the real world is a complex and unpredictable process. And some cultural elements are more homogenous that others. The fact that changes in the subtle specifics of model implementation and parameters give divergent end results would seem to indicate a class of systems that is highly dependent on initial conditions and parameter values.

If interaction is, in fact, partially linked to the degree of shared culture among individuals, it is intriguing to consider the roles, and even potential adaptive value, of rituals and traditions which increase the degree of shared knowledge among participants. “Social” events may accomplish their intended purpose both by allowing people to meet, and by providing a base of shared events as a context for future discussion and interaction. Cultures which manage to maintain traditional events or rituals may be strong because the shared actions and experience of a ritual provide common cultural referents for group identity, a common “dictionary” for description, and a focus for coordinated activity and contact.

Chwe has an interesting discussion of parades and political displays as techniques for creating common knowledge among a constituency: “During the French Revolution, political symbols and rituals were not metaphors of power; they were the means and ends of power itself”… “Since submitting to an authority is a coordination problem, an authority creates ceremonies and rituals that form common knowledge” (Chwe, 1998, p. 51). He points out that one of the main functions of a parade is for the crowed to see itself. Groups often indicate membership, rejection, and alignment though semi-coordinated actions, so mass participation is an endorsement or rejection which is visible to all the participants: everyone knows what they saw, and that everyone else saw it too, and that everyone saw them see it.

A perspective focusing on the role of shared social information in the formation of group structure encourages closer examination of common social features that involve information spread. Gossip can take on an new adaptive role in this framework. Not only would it have strictly informative properties and normative effects through enforcement of cultural mores, but it also would be a means of allowing individuals who are rightly group members but who were not all present at a particular event to share in the common knowledge base. “In order to be recognized as a familiar group member it may be advantageous to acquire certain arbitrary or ritualized behavior patterns” (Nicol, 1995, p. 86). Gossip keeps people from being “left out” and reinforces the structure and distinction between groups along the lines of the actors’ conceptions of the groups. The function of mass culture and media might then have strong effects on the identity and functioning of subgroups. Broadcast media like TV and newspapers can be thought of as conveying normative social information or gossip to a broad population, and might conceivably drive individuals to identify with the broader group at the expense of their local subculture. The media are gossip on a large scale, acting as a unifying and homogenizing force. “The Simpsons” becomes a common cultural referent, a topic of discussion, an explanatory touchstone, and replaces the legends and myths which pertain only to specific subcultures.

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