Decomposition, interdependence and precision in multiattribute utility measurements

Traditionally, parameters of multiattribute utiilty models, representing a decision maker’s preference judgements, are treated deterministically. This may be unrealistic, because assessment of such parameters is potentially fraught with imprecisions and errors. The authors thus treat such parameters as stochastic and investigate how their associated imprecision/errors are propagated in an additive multiattribute utility function in terms of the aggregate variance. Both a no information and a rank order case regarding the attribute weights are considered, assuming a uniform distribution over the feasible region of attribute weights constrained by the respective information assumption. In general, as the number of attributes increases, the variance of the aggregate utility in both cases decreases and approaches the same limit, which depends only on the variance decreases rather rapidly and hence decomposition as a variance reduction mechanism is generally useful but becomes relatively ineffective if the number of attributes exceed about 10. Moreover, it was found that utilities which are positively correlated increase the aggregate utility variance, hence every effort should be made to avoid positive correlations between the single-attribute utilities. The authors also provide guidelines for determining under what condition and to what extent a decision maker should decompose to obtain an aggregate utility variance that is smaller than that of holistic assessments. Extensions of the current model and empirical research to support some behavioural assumptions are discussed.