Networks and Small Groups

Abstract : Homans' insights that interaction and sentiment are in a feedback loop that includes clique formation, social ranking and leadership are formalized and derived from a set of limited assumptions and propositions. Freeman's model of groups is used to detect pure informal groups, those that are not consequential upon anything else than sheer hanging around. It produces a system of cliques and rankings based purely on the rates of transitive triads that may include a third who is only weakly connected to the other two. Two assumptions about motivation in networks - the need for safety and efficacy are then combined with Gould's modeling of asymmetric relations in which members are valued for either intrinsic or extrinsic merits. The ratings tend to cascade according to the "Matthew Effect." Finally, people like to choose others who are more attractive than they are, subject to the condition that too much unrequited love is painful. Gould's Formalization of these ideas for the case of small groups produces, among other results, the consequence that those who are chosen more often than others also tend to direct interaction more towards others with lesser rank, a non-intuitive result observed by Homans, but explained by him in substantive rather than formal terms. The logic of rank further dictates that groups become segmented by structural equivalence. Other results are also summarized. Author : Charles Kadushin, Brandeis University

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