Reinhard Suck
University of Osnabrueck, Germany
Abstract
Categorical judgement is a much used method of data collection. A few scaling procedures have been developed to process these data. In the aftermath of Thurstonean scaling there are random utility like techniques. This fact suggests that there is an approach via polytopes to formulate necessary conditions for random utility representations. In this paper a polytope is defined and investigated which is suited for this purpose. It turns out that it is related to the linear ordering polytope and to the biorder polytope. The relationship is explored. The possibility of independent random utility representations leads to subset of the polytope defined by nonlinear restrictions thus complicating the investigation.