University of Illinois at Urbana-Champaign
This chapter presents a multivariate approach toward modeling preferential choice with a particular emphasis on the method of paired comparisons. Because the method of paired comparisons rests on a minimal number of assumptions, it proved to be applicable across a wide range of disciplines and, consequently, stimulated important work in the areas of experimental design, nonparametric statistics, as well as measurement and scaling. In general, this technique requires that pairs of objects are presented either simultaneously or successively to judges whose task is to indicate which member of the pair they prefer on a specific criterion. The criterion may be overall preference or any attribute that characterizes the choice objects. Judges are not always consistent when making these comparisons. During the last 80 years, several mathematical models were suggested for describing paired comparison responses on a single attribute and, in particular, explaining inconsistencies in pairwise judgments under seemingly identical conditions. David ( 1988) provides a recent comprehensive review of this research. In this chapter, multivariate counterparts of the proposed models are developed that describe paired comparison judgments with respect to multiple attributes.
In a multivariate paired comparison task, information about the choice pairs is obtained by asking subjects to compare objects with respect to several criteria. For example, in the first reported application of a multivariate paired comparison experiment, pharmaceutical products for children were scaled regarding their color, odor, and taste ( Nakagami, 1961). Although multivariate paired comparison data may be examined by analyzing separately each set of paired com