A Measure of Sociometric Reciprocity

Abstract

A measure of reciprocal interpersonal acceptance is developed from the point of view of the mutual acceptance of the members of role sets. The model consists of the application of four basic notions in probability theory. These are: (1) the concept of probability space; (2) the binomial coefficient; (3) the assumption of independence of events; and (4) the binomial theorem. Acceptance is analyzed under two basic conditions: first, under the condition of independence of choice and where everyone in the set rates everyone else; second, under the condition of nonindependence of choice, where a designated number of persons is chosen by each. A general solution was found under the first condition and under the second condition when N/k, the ratio of the total number of persons, N, to the number of persons chosen plus 1, k, is an integer. A general solution was not found when N/k is a noninteger. An ad hoc solution was proposed for this case.