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This paper presents a valence approach for assessing multiattribute utility functions. Unlike the decomposition approach which uses independence axioms on whole attributes to obtain utility representations, the valence approach partitions the elements of each attribute into classes on the basis of equivalent conditional preference orders. These partitions generate multivalent utility independence axioms that lead to additive-multiplicative and quasi-additive representation theorems for multiattribute utility functions defined over product sets of equivalence classes. Preference interdependencies are thereby reflected in these classes, so attribute interactions are readily interpreted and the functional forms of the representations are kept simple. (Author), Revision of report dated Aug 79.

Several advances in multiattribute expected utility theory have emerged recently. Much of the existing theory deals with independence axioms on whole attributes and the corresponding utility decompositions. This paper reviews three alternate approaches for obtaining representations of multiattribute utility functions: (1) multivalent preference analysis, (2) approximation methods, and (3) spanning analysis. Unlike some utility decomposition, these approaches require the assessment of only single-attribute functions which makes implementation relatively simple. Only multivalent preference analysis and spanning analysis, however, provide axioms that can be empirically tested to justify a particular utility representation. (Author)

In eliciting multiattribute utility functions, the valence approach partitions the elements of each attribute into equivalence classes on the basis of conditional preferences. This report establishes equivalence relations for multivalent forms of additive independence, utility independence, and fractional independence, which lead to several new utility representation theorems. When the utility function is continuous, however, some simple partitions are impossible in multivalent preference structures. These results should simplify testing and assessment procedures when attributes are interdependent. (Author), Revision of report dated Dec 78. Prepared in cooperation with Bell Telephone Labs., Inc. Murray Hill, NJ.

This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions: the additive, Keeney's quasi-additive, Fishburn's diagonal, and others. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations which are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes: apex, diagonal, quasi-pyramid, and semicube. The methodology is illustrated with geometric structures that correspond to the fractional hypercubes.

The fractional hypercube decomposition theorem for multiattribute utility functions is used to produce two new decompositions: the pyramid and the semicube. The pyramid decomposition resembles Keeney's quasi-additive decomposition but has nonseparable interactions between every pair of attributes. The semicube decomposition has nonseparable terms for all but the highest order interaction. These decompositions illustrate the diversity of results that can be generated with fractional hypercubes.

This paper integrates existing and new methods for assessing unidimensional expected utility functions in a comprehensive study of utility assessment. It describes briefly and utility assessment process in decision analysis and then reviews problem formulations, sources of bias in preference judgments, and the analysis of risk attitudes. Critically examined are about two dozen utility assessment methods of which half appear for the first time. These methods are grouped under preference comparison methods, probability equivalence methods, value equivalence methods, certainty equivalence methods, hybrid methods, paired-gamble methods, and other approaches. The nature of judgmental biases is emphased in comparing different assessment procedures. Since most multiattribute utility functions are decomposed into single-attribute functions, this study should facilitate such applications.

Some new results in multiattribute utility theory are presented in this report. It is shown how fractional hypercubes induce the multiple element conditional preference orders used to specify attribute independence conditions, and how they also provide a system of equations used to produce the corresponding multiattribute utility decomposition. Fractional hypercube decompositions include most of the previous forms (additive, Keeney's quasi-additive, and Fishburn's diagonal) and give many new utility decompositons (e.g., pyramid, bipyramid, semicube). These new forms model nonseparable attribute interactions, so they are applicable to decision problems in systems analysis, resource allocation, and bundle evaluation, among others. (Author), Sponsored in part by National Science Foundation, Washington, D.C., Grant NSF-GP-32314.