Preference Inference with Additive Multi-Attribute Value Models and Holistic Pair-Wise Preference Statements

Additive multi-attribute value models and additive utility models with discrete outcome sets are widely applied in both descriptive and normative decision analysis. Their non-parametric application, robust ordinal regression, allows preference inference by analyzing sets of general additive value models compatible with observed or elicited holistic pair-wise preference statements. In this paper, we provide necessary and sufficient conditions for preference inference based on a single preference statement, and sufficient conditions for preference inference based on multiple preference statements. The sufficient conditions in the multiple statement case are precise enough to infer everything possible in our numerical experiments. Moreover, our analysis suggests that mutual preferential independence is a too weak condition alone to be useful alone in practical decision support where preferences are elicited in form of holistic statements.

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