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In this paper, a method for systematically assessing multidimensional situations is developed. More precisely, the psychophysical method of "interpolation between the corners" suggested by Yntema and Torgerson is formalized. It is proven that, subject to von Neumann and Morgenstern's axioms of "rational behavior" and the quasi-separability assumptions, the utility (or worth) of a multidimensional situation may be evaluated from sums and products of the utilities of single-dimensional situations. After developing the necessary methodology, a hypothetical problem is considered in order to illustrate the use of this approach and to indicate its potential for applications.