Die Entropiemaximierung von A.G. Wilson: Kritische Thesen zur Gültigkeit einer Interaktionstheorie

Abstract

The entropy-maximizing framework is known as an important concept in developing the theory of interaction. Although this technique was already introduced by Wilson in 1967, it is still today the most accepted theory for macroanalytic interaction models and is widely used in science and practice. After a short description of the derivation of the double-constrained model, three fundamental parts of the entropy-maximizing method not only valid for the basic model but for all derivatives are picked out for a detailed analysis: the family of gravity models, the use of different cost functions and the analogy with thermodynamics. It is shown that the derivation of the double-constrained case alone can be regarded as valid, but it is impossible to derive the other members of the family of models. Wilson's reformulation of the derived cost function as net benefit' is not part of the optimization process and is there fore not consistent with the entropy-maximizing frame work. Apart from this, the mathematical treatment is incorrect. The use of different cost functions is not admissible, because the result of the optimization process is one specific cost function, the negative exponential, which is based on the partial derivation of the third constraint equation about the total cost C. Any change of the cost function implies a modification of the constraint equation. So the process is turned upside down. The third part of the analysis, the analogy with thermodynamics, shows that the analogy is not true. It is not adequate to compare the movement of gas molecules with human behaviour because people do not tend to spread out regularly over the whole system to get a state of maximum disorder. Indeed, the decision behaviour depends only on the alternative destinations and not on the other origins or the whole system respectively. Finally some empirical examples are explained. The functional relationship between the input parameter total cost C and the spatial impedance factor ß proves to be quite insensitive over a wide range and becomes very sensitive near the cost minimum. The consequences of this relationship are illustrated by cartographic figures. As the result of the analysis it can be stated that, in contrast to the sophisticated approach, there are too many deficiencies in Wilson's entropy-maximizing concept to retain the validity of this interaction theory any longer.