Equivalence: Social roles

Hanneman and Riddle, Chapter 15.

• Social roles
  • Basic building block - norm and sanctioned expectation sets
  • Identities as the sum of social roles
  • Social roles are relational
    • Describe norms governing relations among classes of actors
    • E.g. "worker-capitalist," "core-periphery," "banker-customer," "in-group member versus "stranger"
• Regular equivalence
  • Same pattern of relations with same other types of actors
  • E.g. "A mother" versus "My mother"
• Visualizing regular equivalence
  • Graphically: The Wasserman-Faust network, complexity in "real" networks
  • Numerically:  Blocking and permutation
• Two examples:
  • Padgett's Florentine marriage alliances
  • Knoke's information exchange
• So what?
  • Social roles define expectations, norms, and sanctions -- powerful predictors of individual behavior
  • Patterns of social roles and their interconnections in a population define the differentiation and integration of the relations among roles -- not individuals.  Abstract view of "society."
  • Variability of individuals within roles may tell us something about conformity and deviance, the "flexibility" of social structure

1. Define the concept of a social role, and provide an example.

2. What does it mean when we say that "regular equivalence" provides a "relational" approach to describing social roles?

3. Suppose two actors are regularly equivalent.  Are they also structurally equivalent?  Suppose that two actors are structurally equivalent.  Are they also regularly equivalent?  Explain.

4. Sketch an example of what a permuted adjacency matrix would look like if it were describing perfect regular equivalence among three sets of actors, with three actors in each role.

5.  Are the actors in a clique regularly equivalent?  What about the actors in a "star," a "line," and a "circle" network?

Application Questions

1. Think about friendship ties among students in a class.  What would it mean to say that several students were "regularly equivalent?"  Think about an ideal typical "market."  Are there "regularly equivalent" sets of actors here?

2. Think about the labels that you use to describe members of your kinship group (family).  What are the "kinds" of people?  Describe the relation of "gives advice to" among the regular equivalence categories you identified.

3. Think about the labels that are used to describe some major stratification variables (e.g. gender, ethnic, "racial," religious, political, social class).  To what extent are these labels describing relational "regular equivalence" classes?  What are the relations that define the differences among the groups?

4. Consider our classical hierarchical bureaucracy, defined by a network of directed ties of "order giving" from the top to the bottom. Make an adjacency matrix for a simple bureaucracy like this. Block the matrix according to regular equivalence sets.

5.  Consider world commodity markets -- for example, oil.  Are there sets of regularly equivalent actors present?