Abstract:
Some groups endure longer, are more stable, and are better able
than other groups to incorporate new members or ideas without losing their
distinctiveness. I present a simple model of individual behavior based on the
thesis that interaction leads to shared knowledge and that relative shared knowledge
leads to interaction. Using this model I examine the structural and cultural bases
of group stability. Groups that are stable in the short run do not necessarily
retain their distinctiveness in the long run as new members enter or new ideas
are discovered.
Hypothetical
narrative
Consider two companies.
One is small (few members who interact often), socially
undifferentiated (they come from similar backgrounds and have similar view
points), and culturally homogenous (they have similar views on how to solve
problems and work as one big team).
The other is large (many members who interact less often),
socially differentiated (they come from different backgrounds), and culturally
heterogeneous (they often split into subgroups to handle multiple clients).
Both are considering hiring a new person to move into a new
area of work. Will the addition of a new member or new information destabilize
these groups? What are the structural and cultural bases for group stability? For
example, what types of groups are the most stable? What types of groups are
least affected by the addition of new members? What types of groups are least
affected by expansion of the group's knowledge base?
A “Constructural” Perspective:
- Groups can be defined by shared social, demographic, or sociocultural features (e.g., Catholic boys age 13).
- Each position on a social dimension is associated with a particular body of knowledge that is acquired by individuals with that characteristic (e.g., Catholics learn the tenets of Catholicism, the order of the mass, etc.). It is the wealth and uniqueness of the information associated with that dimension, not the dimension per se, that determines behavior.
- Group characteristics and behavior are derived from the characteristics an behaviors of the group members. Three axioms of this relationship:
- Individuals are continuously engaged in acquiring and communicating information
- What individuals know influences their choices of interaction partners
- An individual’s behavior is a function of his or her current knowledge
- Groups form and endure because of discrepancies in who knows what.
- Groups are typically in flux simply because members are continually acquiring new information and communicating it to each other. Therefore, a group is perfectly stable only when no new information enters the group and everyone in the group knows everything that anyone else in the group knows.
- From this perspective, neither institutional nor motivational factors are necessary for group stability, nor is a differentiated environment or a differential set of institutional or motivational factors necessary for distinct groups. Rather, these factors may serve as secondary forces modifying the impact of the primary force: interaction and the exchange of information.
- Institutions can maintain their identity, stability, and cultural distinctiveness by preventing the flow of information.
Using a simple model, the author explores group stability
and endurance in one-group and two-group societies in which there is no change
in group membership and no new ideas. She then examines the ability of these
groups to assimilate a new member or idea without losing their uniqueness as a
group.
Basic Model
A population of
size I constitutes a society. A group is any subset of the society.
The society has a culture. The society contains a number of facts, K, that the individuals can
learn. The number of available facts determines the complexity of the culture. An individual either knows a fact or
doesn’t at any given time.
Stages of the cycle
of interaction:
- Action:
- Dyads with high levels of interaction (e.g. friends) have more shared knowledge, and this tends to increase over time.
- Simplification: all facts are independent, all interactions are dyadic, and all facts known to an individual are equally likely to be communicated.
- At time t, Agent i communicates fact k to Agent j if they interact and if Agent i chooses to communicate with Agent j. If so, a fact is chosen at random from what i knows.
- The functions for who is chosen to interact and whether a fact is communicated are pretty vaguely described.
- Adaptation
- Really nothing. Agents don’t forget facts, they don’t learn them on their own, and they don’t miscommunicate them.
- Motivation
- Individuals are more likely to interact with similar others. “The point of constructural theory is that an individual’s perception of his or her motivation to interact is not the determinant of interaction; rather, it is the sheer volume of what each individual has in common with other individuals relative to how much he or she has in common with everyone else that determines interaction.”
- In previous formulations, similarity is determined by the number of dimensions that people have in common.
- Carley extends this in several ways
- The weaker the tie, the lower the probability of interaction
- Different “points” on each dimension have an associated body of knowledge, such that each individual at that point has a certain likelihood of knowing (NOTE: huh?)
- Similarity is defined in terms of shared knowledge (effectively weighting the dimensions)
- Interaction is predicted in terms of relative similarity.
- Relative similarity is related to interaction thusly: The probability that individual i interacts with agent j at time t is a function of how much information is shared between i and j, relative to the sum across the population of how much information i shares with each member of the society. The model assumes that all agents know how much information they share with each other agent.
Measures of Stability
- Perfect stability: An equilibrium that occurs only when no new information is entering the group, there are no changes in the distribution of information, and there are no changes in interaction probability. Everyone in the group knows the same stuff.
- Time to stability: The number of time periods until the society reaches perfect stability. The longer this takes, the less stable the society (NOTE: not sure about this definition).
- Endurance: This only makes sense in a multigroup society. A group endures as a distinct group as long as its members are more likely to interact with each other than with individuals outside their group. The endurance time for a group is the number of time periods until the probability of intragroup interaction is greater than the probability of intergroup interaction.
- Cultural homogeneity: This is a combination of two other measures: connectedness and diversity.
- Any two individuals or groups that share at least one fact are connected. Two groups can be disconnected only if no pair of individuals, one in each group, shares any knowledge. A society in which there are no disconnected groups is “fully connected.”
- Cultural homogeneity is measured by the percentage of possible dyadically shared facts (i.e., all possible combinations of dyads and facts) that are actually shared.
Summary of model
facts:
For a society with an initial distribution of knowledge,
stability is always achieved.
The stable society is one in which a specific sociocultural
configuration exists and does not oscillate (a single limiting state).
Every society eventually becomes perfectly stable, and may
contain multiple groups that will coexist indefinitely as distinct, because
each group has a monopoly on its facts.
Results: One-group
societies
For one-group societies, the population converged more
quickly when (1) there were fewer facts to know, and (2) a higher percentage of
facts were known by the agents. Population size did not affect the time to
stability, because the larger the group, the more people there are to tell
people both what they do not yet know and what they already know. In contrast,
the simpler the culture (the fewer facts available) the more quickly society
reaches stability because there is less for people to learn. Furthermore, the
more homogeneous the culture, the more quickly stability is reached because
there is proportionally less to learn.
Results: Two-group
societies
For a connected society, the mark of stability here is
endurance (as defined above). Each group had either 6, 12, or 18 agents, and a
total of 10, 20, or 40 facts. Each group had a monopoly on half the facts,
except that one agent in each group knew one fact that was known by one member
of the other group. These two individuals were tied weakly and acted as a
bridge between the two groups.
Again, the population size did not matter, and the number of
facts was positively correlated with the average endurance time.
Group size ratio and cultural overlap: Simulations
were run with 2 societies, with 24 agents split between them, and 40 facts.
Each group had a quasi monopoly on half the facts. Group size ratios were 1:1
(6:6), 1:2 (4:8), and 1:5 (2:10). The percentage
of the other group’s facts were equal for the 2 groups, and could be between 10
and 75%. A higher skew in size ratio led to longer endurance, as did a smaller
amount of shared knowledge.
When a new person enters the society. Here the groups
were as in the above two-group experiments. A new person was added to one group
(the minority, if there was one), and knew only one fact, which was already
known by all members of the group.
Adding a new person to a two-group society decreases the
group’s endurance considerably. The new person has less impact the larger the
population, the fewer the facts, the more distinct a group’s set of facts, and
the closer the two groups are in size.
Adding a new fact. For two-group runs, one individual
(in the minority group if there was one) was given a new fact.
The new fact tended to increase the group’s endurance
slightly.
“This point suggests that as groups develop ‘things’ that
increase their cultural distinctiveness…, such as inventions, discoveries, new
works, or new rituals, they increase their endurance (and hence their stability
as a group). Discoveries, however, also increase the variance within the group
in terms of who knows what, and thereby decrease the probability of intergroup
interaction.”
Concluding thoughts.
The model is neat. It’s an early model, and the analysis is
not that sophisticated, but the basic idea is feedback between homophily and
interaction drives group cohesion and polarization, which is a very important
point.
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