Is the whole different from the sum of its parts? A proposed procedure for measuring divergence from additivity

The behaviour of many small systems, such as a family or a football team, epitomizes the famous Gestalt slogan of a “Whole which is different from the sum of its parts”. However, and in the context of these small cognitive systems, conceptualizing and measuring the extent and the way in which a whole is different from the sum of its parts is a non-trivial challenge. One possible direction for addressing this challenge involves measuring the extent in which the entropy of the whole is non-additive, meaning different from the sum of the entropy of its parts. However, measuring divergence from additivity is far from trivial. In this short paper, we propose a simple procedure for measuring divergence from additivity and illustrate the procedure by analysing the behaviour of a soccer team.