The Facets of Place

This chapter will outline one theory aimed at integrating aspects of environmental psychology with issues in architectural design. The theory to be reviewed is broad in those characteristics of theory that Moore (1987) called their 'form and scope'. This broad brush, top down approach is intended as a contrast with bottom up attempts to specify the behavioural effects of specific aspects of design, such as lighting levels or size of spaces. It also contrasts with models that seek to answer immediate design problems. However, in Moore's (1987) vocabulary, the theory to be outlined is more than an 'orientation', or 'framework'. It is an 'explanatory theory' that has been found to have considerable scope, open to direct empirical test

Primary Facets Of Order Polytopes

Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all order relations of a chosen type. The five prominent types of order relations are linear orders, weak orders, semiorders, interval orders and partial orders. For each of them, the problem of finding a complete, workable characterization of the vectors of probabilities is crucial---but it is reputably inaccessible. Under a geometric reformulation, the problem asks for a linear description of a convex polytope whose vertices are known. As for any convex polytope, a shortest linear description comprises one linear inequality per facet. Getting all of the facet-defining inequalities of any of the five order polytopes seems presently out of reach. Here we search for the facet-defining inequalities which we call primary because their coefficients take only the values -1, 0 or 1. We provide a classification of all primary, facet-defining inequalities of three of the five order polytopes. Moreover, we elaborate on the intricacy of the primary facet-defining inequalities of the linear order and the weak order polytopes