A Taylor-Polynomial Representation of Value Functions for Multi-Attribute Decision Strategies

Abstract

Decision strategies in multi-attribute decision-making are described as qualitatively distinct rules with no common quantitative scale for comparing them. This study proposes a unified framework that represents a decision strategy as a feature vector built on a Taylor-polynomial value function, placing strategies in a common space of value functions whose coefficients describe their local sensitivity structure. The value a strategy assigns to each attribute is approximated by a Taylor polynomial about a common expansion point and embedded in a softmax choice model. The model is fitted by penalized maximum likelihood to the choices of eight standard decision strategies and a random-choice baseline, simulated across decision environments differing in the number of alternatives and attributes, weight dispersion, and dominance structure. Each strategy is summarized by a feature vector that holds a weight sensitivity, a decisiveness parameter, and Taylor coefficients of degree at most four. The recovered shapes were linear for the additive and lexicographic strategies and boundary-localized concave or convex for the cutoff strategies, consistent with their qualitative definitions. Choice reproduction was exact for the additive strategies and the lexicographic (LEX) strategy, high for the lexicographic semi-order (LEX-S) strategy, partial for the cutoff strategies, and at or below chance for the disjunctive strategy. The Taylor coefficients therefore give a common feature space in which decision strategies are described, compared, and classified.