A Rationale for Additive Decomposition in Multiattribute Utility Assessment

Abstract

The purpose of this paper is to develop a rationale for the decomposition of a hierarchy of objectives used as the basis for the assessment of a multiattribute utility function. This rationale is based on a comparison of two approaches to the assessment of multiattribute utility functions. One is simply to interrogate the individual whose preferences regarding a given outcome are to be elicited, and obtain an intuitive estimate of the desired utility. This is termed the wholistic estimate, because the different attributes are considered all at once, and no decomposition is attempted. The second alternative is to decompose the problem into several single attribute assessment problems, and then obtain the multiattribute utility function using an appropriate aggregation rule. The advantages cited for this approach are the usual ones associated with any decomposition strategy. A greater degree of systematization is introduced into the assessment problem. Individual problems are smaller and easier to solve, and their solutions can be combined mechanistically using a suitable aggregation rule. However, with each of these assessments one can associate some error, and when the assessments are combined to obtain the decomposition estimate, the combined error might be significant. An analysis of the errors associated with the wholistic and the decomposition strategies will be used to identify when decomposition into a hierarchy of objectives is an appropriate strategy.