SOME SIMPLE MATHEMATICAL MODELS FOR ADOPTION PROCESSES: THE CASE OF THE COMPREHENSIVE SCHOOL REFORM IN NORWAY.

In this article, the authors have considered some simple models for the diffusion of innovations, using as an illustration the adoption of the comprehensive school reform by Norwegian communes. The first aim was to present a kind of catalogue of models showing for which technical reasons some models tend to appear rather often and which could serve to lead, if necessary, to more complex models. The second aim was to define and limit for each model the kind of explanation it suggested. Two possible models, which have been most frequently proposed in the literature, will be emphasized. Descriptive models serve first to summarize data. The shape of the diffusion curve when fitted to a function which has a simple analytical form as well as few parameters is more easily remembered than if it had a more precise empirical description. The exact analytical form is not so important because different functions can serve the purpose of fitting the data reasonably well. Usually, analytical formulas are chosen according to the author's familiarity with them. Probabilistic models allow for more refined hypotheses than deterministic models, and, in principle, they also allow for a better judgement about the quality of fit. This, however, occurs only in the framework of a number of assumptions where control might be difficult. Probabilistic models generate a distribution of diffusion curves: the observed one being one among numerous possibilities.