| Abstract: | An extension of Heiderian triadic balance (Heider, 1946, 1958) for quantitative data is presented and an algebraic formula is developed: M′ = m - s - 1, s, m, 1 denoting the smallest, medium, and largest of the relations of a triad; lower values indicating more positive relations than higher ones. M′ can be interpreted as a natural structural characterization of a triad which covers the idea that balance is an interaction effect of attraction and agreement in a triad. The formula is applied to the sociometric ratings (P-O-Q triads) of the members of seven peer-groups. AS predicted, the higher the value of M′ the more the empirical frequencies of triads exceed their expected chance frequencies. The formula is compared theoretically and empirically with other balance models for quantitative data (Osgood and Tannenbaum, 1955; Morrissette, 1958; Wiest, 1965). In the P-O-Q situation the formula presented is shown to be superior to the other models. Finally some substantial problems related to balance are discussed and a second interpretation of M′ is given: M′ is an equal weight linear combination of four functions which can be seen as group forming forces in triads (forces towards group integration, towards tight friendships, and two clique building forces). |
