Mark (1998) Beyond individual differences: Social differentiation from first principles.

Mark N (1998) Beyond individual differences: Social differentiation from first principles. American Sociological Review 63:309-330. 

The paper attempts to provide a formal explanation for the emergence of social differentiation. An important characteristic is that it does not require an assumption of initial differences in natural endowments or structural positions of individuals.

NOTE: this is a really well written and thoughtful paper.

The theory: systems tend toward social differentiation for two reasons:

1. Individuals have a limited capacity to process information. This constrains them to interaction with a reduced set of others. 
2. The stochastic process by which individuals are paired in relations generates differences in the information encountered by different individuals. 

The theory (allegedly) has three properties that are desirable of any theory (from Jasso 1988): 

1. That the assumption set be as short as possible

2. That its observable implications be as many and as varied as possible

3. That its observable implications include phenomena or relationships not yet observed. 

Some factors theorized to influence social differentiation. 

1. Population growth, which increases the logistical load faced by a society. Differentiation is a necessary response to these increased demands. 
2. Technological advances have both positive and negative effects. 
• Advances raise productivity by introducing processes that involve some degree of specialization, and have indirect effects through the creation of administrative and distributive needs, creating subsystems to meet these needs. Increases in population size and density are also repercussions of some tech advances. 
• Technology and larger, more dispersed systems also promote cultural similarity and high rates of interaction between people in different subsets of society, thereby reducing social differentiation. 
3. Wealth has also been theorized to increase social differentiation.

A Theory of Information and Social Structure

• Information is assumed (for simplicity) to exist as discrete pieces that can be independently known. For any person at any particular time, a piece of information can be either known or unknown.
• Similarity: Individuals with similar information are more likely to interact.
• Communication: Individuals communicate information to each other in the process of social interaction.
• Information creation: Individuals create information in the interaction process. NOTE: This is different from people simply sharing information, it seems, and represents a key difference between this and Carley’s (1991) model.
• Forgetting: Individuals forget information that they have not expressed in interactions for an extended period of time. NOTE that there is substantial societal variation in information technologies used to store and manage information, creating variance in the effective time to forget.
• Technology and the forgetting assumption interplays with the similarity assumption. Technology allows people to keep more social ties, and to retain more information, which may sustain similarity between individuals and increase the likelihood that they meet up.

The Model

Social interaction occurs in rounds, each with three steps: (1) the selection of interaction partners; (2) social interaction; (3) forgetting.

1. Selection of interaction partners
• Each agent picks a potential interaction partner. The probability that person A initiates an interaction with person B is the number of facts they have in common, divided by the sum of the number of facts that A shares with each person in the system (following Carley, 1991). 
2. Interaction
• In an interaction, the union of the two individuals’ sets of facts becomes a pool from which one fact is chosen for expression. Alternatively, the interactants may create a new fact. A newly created fact is always unique – two people cannot create a fact that other people have already created.  
• Each fact from the known pool has an equal probability of being expressed, which is equal to the probability that a new fact is created. 
3. Forgetting
• If an individual goes through a set number of consecutive rounds without expressing a particular fact in an interaction (including self-interactions), the individual forgets the fact. 

Social differentiation is defined as the degree to which interaction occurs within distinct sets of individuals, between which sets there is little interaction. An undifferentiated system is one in which interaction is equally likely between all pairs of individuals (including self-pairs). According to the model, social structure is undifferentiated when all individuals know exactly the same information.

The emergence of social differentiation

The model can produce social differentiation between two groups even when the population starts as one group in which everyone knows the same information.

He starts with 4 individuals who all know one fact (Figure 3). Now suppose agents interact in pairs AB and CD, and each pair creates a new fact. Now there is differentiation between these pairs, but the society is still connected, via Fact 1 (Figure 4). “Because interaction between A and B and between C and D is more likely than is interaction for other dyads (e.g., A and C), the probability that new information will be created in the AB and CD dyads relative to other dyads is higher than it originally was. Any new information created in the AB and CD dyads will strengthen the tendency for these individuals to continue to interact within their respective subgroups (AB and CD). As sub- group-specific information grows, any fact that all four have in common becomes a weaker integrating force relative to the growing separating effect of subgroup-specific information.” In other words, they may forget facts that united them with the other subgroup. If there were only one (or few) of these, the subgroups may become disconnected (Figure 5). 

Simulations

500 rounds of interactions. At the beginning of each simulation, only one fact exists, which all individuals know. Population sizes of 6, 50, and 100 were tested, with three memory levels: 3, 4, and 5 rounds (all individuals have the same memory in each simulation). 60 simulations were run for each parameter combo.

The dependent measures were:

• Cultural homogeneity: Homogeneity for a given fact is the number of pairs of individuals for which both individuals know the fact divided by the total number of pairs of individuals. Cultural homogeneity is the average homogeneity across all facts in the system. 
• Social differentiation: This is the number of groups into which a system has split after 500 rounds. Groups are defined as sets of individuals which are all connected, but disconnected from other groups. For systems that remain fully connected, the value of social differentiation is 1. 
• Group size: The mean size of groups after 500 rounds. I.e., the system size divided by social differentiation. 

Results

• Cultural homogeneity was negatively affected by system size – as system size increased, cultural homogeneity decreased. Memory had a positive effect on cultural homogeneity. The more memory, the better cultural homogeneity is able to be maintained. 
• Social differentiation. 
• As the system size increased, so did the social differentiation. In part, this was probably due to a larger population being able to split into more groups. 
• As individuals’ memory capacity increased, social differentiation decreased. This effect was pretty dramatic. 
• The effect of system size was pretty much eliminated if the memory capacity was large. This indicates that when memory is high enough for large systems to remain connected, decreases in size do not reduce differentiation.