An Examination of Conditional Violations of Axioms for Additive Conjoint Measurement

Axiomatic conjoint measurement methodology of fers a useful approach for evaluating different compo sition rules as potential models for fitting the compo nents of multidimensional stimuli. The usefulness of this methodology has been somewhat hindered in ap plied settings because of a lack of an adequate error theory for testing the fit of data to the axioms. This paper presents the results of an attempt to provide a basis for an examination of errors of the conjoint mea surement axioms. Specifically, this paper describes a means of evaluating the fit of an additive conjoint measurement model to a three-factor design. For each of the critical axioms of axiomatic conjoint measure ment, the proportions of errors that would be expected by chance for different levels of satisfaction of the simple independence property are examined. The re sults indicate that violations of these axioms occur much less often than intuitively might be expected. Error proportion tables based on monte carlo analyses are presented to aid in comparisons with empirically obtained results. It is shown that two types of viola tions of the axioms can be defined and used to differ entiate between systematic and unsystematic errors in fallible data.