Estimation of Individual Level Multi-Attribute Utility from Ordered Paired Preference Comparisons

Abstract

Ordinal preference measures have a number of advantages relative to cardinal measures in the estimation of individual level multi-attribute utility functions. This paper: (a) outlines a theoretical foundation for estimating a cardinal scaled utility function from ordinal preference data, in particular, pairs of pairs or ordered categorical comparisons; (b) forwards two linear programming procedures designed to estimate individual level attribute weights from such data; (c) evaluates the statistical properties of these estimators; (d) develops statistical significance tests for the proposed estimates; and (e) evaluates the ability of these estimators to predict hold out sample preferences for two real world datasets. Simulations show that our ordinal preference-based weight estimates more closely approximate the true weights and are more robust to data quality than either regression or logit. Our real world results also show superior predictive performance. Furthermore, in most cases, these findings are true even when the latter methodologies are augmented using Hierarchical Bayes techniques. Clearly, the higher potential for measurement error and scale usage heterogeneity that resides in cardinal scaled data is an issue. Correspondingly, ordinal preferences in conjunction with our linear programming estimation methodology provides individual level attribute weight estimates that are worthy of academic and managerial attention.

Keywords: Cardinal Utility Functions, Attribute Weights, Ordered Paired Comparisons, Linear Programming, Conjoint Analysis