The Davis-Moore theory of social stratification (1945) argues that inequality is due to differences in the ‘importance’ of social rôles, and that recruitment to important social rôles will be more oriented toward getting adequate performance than will recruitment to other rôles. Importance of rôles, then, tends to create inequality and to create a force toward recruitment by ability and training. One of the difficulties in working with this theory empirically is to obtain independent measures of the importance of social rôles.

In this paper we will treat the importance of supervision in the productivity of groups. We will show that for groups doing highly interdependent tasks, the marginal productivity of added amounts of supervision (starting from any given level of supervision) will be higher than in groups doing independent tasks. Further we will show that the ability of a supervisor is more important in determining group productivity in the interdependent case.

The derivation of these results will be purely theoretical. If actual stratification systems (in small groups, factories, or societies) actually behave as the Davis-Moore theory implies, then the machinery here will help derive predictions about the relation of task structure to stratification structure. This involves defining the importance of a social rôle by how much difference its performance or nonperformance makes to total group performance, and by how much difference it makes to group productivity whether it is well performed or not.