A Fundamental Limit on Productivity in Organizations Collaborative Entropy Costs

Many researchers and managers agree that small workgroups tend to lose productivity and speed as they grow large and that decision-making tends to become sluggish in very large organizations. These effects are attributed to collaborative coordination costs that grow in importance as functions of an organization’s scale. Understanding of these effects has however been primarily empirical and qualitative. This paper presents a first-principles mathematical model that quantitatively predicts such productivity variations. It is based on a fundamental cost mechanism that has been overlooked in the past but which nonetheless dramatically limits knowledge workers’ productivity and timely response: one must account for the information associated with each actor’s range of collaborator choices when trying to understand organizations as systems of human knowledge processors. A Shannon-like “collaborative entropy” is quantified and introduced to model the extra decision information that must be generated when an organization distributes its functions among collaborating internal actors. The implied coordination cost is a fundamental limit on the per capita productivity for knowledge work. The productivity limit would apply even if management made perfect resource allocations. Information is lost if actors try to exceed the maximum rates for exchanging decision information. The model compensates for value gained by accessing specialized expertise and hiding complexity. The productivity metric used assumes constant decision quality. In a single growing workgroup the per capita productivity increases while the group is small and lightly loaded, but it falls off logarithmically rather than remaining constant once the group size exceeds a saturation value at which raw decision capacity is all in use. The productivity fall-off is due entirely to collaborative entropy. For organizations as a whole two additional scale effects may apply: the fraction of an actor’s total effort spent in collaboration versus individual work may grow, and the average number of collaborators per actor may also grow owing to increasing specialization. Productivity is then strongly peaked around an optimum organization size and varies rapidly above or below the peak by a factor in the range of 2 5. The productivity impact of collaborative entropy is large enough to strongly affect competitive advantage. Impact is maximized when the ratio of collaborative to individual effort is large. Large organizations may thus be inherently disadvantaged versus small ones wherever fast decision-making or high knowledgeworker productivity are key drivers. Even a modest amount of collaboration significantly decreases the productivity of actors functioning primarily as individual contributors.