UTILITY THEORY VIOLATIONS BY MULTI-CRITERIA HIERARCHICAL WEIGHTING METHODS

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Abstract
This paper discusses two violations of utility theory that can arise with some common multi-criteria hierarchical weighting methods when employed for selection of the best of several alternatives considering multiple criteria. First, these hierarchical weighting methods are found to violate utility theory's principle of independence of irrelevant alternatives. Proof of this violation is made by counter-example. Second, a common violation of additive utility exists even when only two alternatives are considered, a case without irrelevant alternatives. The frequency of this incompatibility of hierarchical weighting with additive utility is explored through a numerical experiment and found to range between 4% and 13% for different problem sizes. These problems do not exist for application of weighting methods to single-objective problems.