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6 Block Modeling
1. Block Modeling Overview Social life can be described (at least in part) through social roles. To the extent that roles can be characterized by regular interaction patterns, we can summarize roles through common relational patterns. Social life as interconnected system of roles Important feature: thinking of roles as connected in a role system = social structure
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3. Coherence of Role Systems Necessary : Some roles fit together necessarily. For example, the expected interaction patterns of “son-in-law” are implied through the joint roles of “Husband” and “Spouse-Parent” Coincidental : Some roles tend to go together empirically, but they need not (businessman & club member, for example). Distinguishing the two is a matter of usefulness and judgement, but relates to social substitutability. The distinction reverts to how the system as a whole will be held together in the face of changes in role occupants .
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5. Family Structure Start with some basic ideas of what a role is: An exchange of something (support, ideas, commands, etc) between actors. Thus, we might represent a family as: H W C C C Provides food for (and there are, of course, many other relations inside the family) Romantic Love Bickers with
9. Alternative notions of equivalence Instead of exact same ties to exact same alters, you look for nodes with similar ties to similar types of alters
10. Basic Steps: Blockmodeling In any positional analysis, there are 4 basic steps: 1) Identify a definition of equivalence 2) Measure the degree to which pairs of actors are equivalent 3) Develop a representation of the equivalencies 4) Assess the adequacy of the representation 5) Repeat and refine
15. Regular Equivalence: There may be multiple regular equivalence partitions in a network, and thus we tend to want to find the maximal regular equivalence position, the one with the fewest positions.
27. Padget and Ansell: “ Robust Action and the Rise of the Medici” Medici Takeover
28. Padget and Ansell: “ Robust Action and the Rise of the Medici” The story they tell revolves around how Cosimo de’Medici was able to found a system that lasted nearly 300 years, uniting a fractured political structure. The paradox of Cosimo is that he didn’t seem to fit the role of a Machiavellian leader as decisive and goal oriented. The answer lies in the power resulting from ‘robust action’ embedded in a network of relations that gives rise to no clear meaning and obligation, but instead allows for multiple meanings and obligations.
29. A real example: Padget and Ansell: “ Robust Action and the Rise of the Medici” “ Political Groups” in the attribute sense do not seem to exist, so P&A turn to the pattern of network relations among families. This is the BLOCK reduction of the full 92 family network.
31. Generalized Block Models The recent work on generalization focuses on the patterns that determine a block. Instead of focusing on just the density of a block, you can identify a block as any set that has a particular pattern of ties to any other set. Examples include:
33. Compound Relations. One of the most powerful tools in role analysis involves looking at role systems through compound relations. A compound relation is formed by combining relations in single dimensions. The best example of compound relations come from kinship. Sibling Child of Sibling 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 Child of 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x = Nephew/Niece 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S C = SC
34. An example of compound relations can be found in W&F. This role table catalogues the compounds for two relations “Is boss of” and “Is on the same level as”
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