A comparison of two normative choice formulations: The Shapley Value versus the weighted additive rule

Abstract

The Shapley Value, a cooperative game theory model, is adapted for use as a category preference measure in marketing. The model collects overall ratings for bundles of choices. These are then decomposed into individual preference scores by estimating the average marginal contribution of each choice over all applicable bundles. The technique provides a holistic rating alternative to constant sum for estimating preferences. It is applicable where choices are disparate, incommensurable, and apportionment difficult, where the questioning might gain from indirection or obfuscation, or where unambiguous attribute sets are not available. It provides a metric in circumstances when respondents are reluctant to choose between alternatives, but when one can elicit ratings (that do not appear to yield preference orderings). The Shapley Value is compared to weighted additive and indirect share preference models based upon proximity to a constant sum standard. Proximity is measured by two distance metrics: a Euclidean distance and a directional cosine (correlation) measure. Statistical testing demonstrates that Shapley Value is significantly closer to constant sum than either weighted additive or indirect share in two categories--fast food restaurants and actors in Seinfeld. Testing was conducted in a computer-aided laboratory setting. Subjects were 93 undergraduate business majors enrolled in an introductory marketing course. They were compensated for their participation with both a monetary and course credit incentives.