Accounting for structural patterns in construction of value functions: a convex optimization approach

A common approach in decision analysis is to infer a preference model in form of a value function from the holistic decision examples. This paper introduces an analytical framework for joint estimation of preferences of a group of decision makers through uncovering structural patterns that regulate general shapes of individual value functions. We investigated the impact of incorporating information on such structural patterns governing the general shape of value functions on the preference estimation process through an extensive simulation study and analysis of real decision makers preferences. We found that accounting for structural patterns at the group level vastly improves predictive performance of the constructed value functions at the individual level. This finding is confirmed across a wide range of decision scenarios. Moreover, improvement in the predictive performance is larger when considering the entire ranking of alternatives rather than the top choice, but it is not affected by the level of heterogeneity among the decision makers. We also found that improvement in the predictive performance in ranking problems is independent of individual characteristics of decision makers, and is larger when smaller amount of preference information is available, while for choice problems this improvement is individual-specific and invariant to the amount of input preference information