David B. MacKay

A Thurstonian view of the analytic hierarchy process

Abstract The application of deterministic decision models in situations characterized by noise and uncertainty is likely to produce results of questionable value. In this paper, some very simple probabilistic models are developed and substituted for the deterministic scales used in the Analytic Hierarchy Process (AHP). It is shown that the use of these probabilistic models can extend the domain of AHP to situations, such as consensual or group decision making, that possess significant amounts of uncertainty. In addition, explicit measures of the variation present in the evaluation of decision alternatives and attributes are obtained.

International differences in product perception: a product map analysis

Shows that traditional product mapping methods for product positioning analysis fail in international settings due to the high variability of product preferences within each country and the lack of a common product perception among countries. Shows how explicitly incorporating variation in the product positioning analysis can overcome both of these problems. Uses a comparison of how Japanese and US consumers differ in their perceptions of the gift market for young males to illustrate how the proposed method differs from traditional methods. Indicates that Japanese consumers perceive the gift market much more uniformly than Americans.

Parameter estimation for the thurstone case III model

A Monte Carlo study was conducted to investigate the ability of three estimation criteria to recover the parameters of Case V and Case III models from comparative judgment data. Significant differences in recovery are shown to exist.

Percept Variance, Subadditivity and the Metric Classification of Similarity, and Dissimilarity Data

AbstractPercept variance is shown to change the additive property of city-block distances and make city-block distances more subadditive than Euclidean distances. Failure to account for percept variance will result in the misclassification of city-block data as Euclidean. A maximum likelihood estimation procedure is proposed for the multidimensional scaling of similarity data characterized by percept variance. Monte Carlo and empirical experiments are used to evaluate the proposed approach.

Extentions of probabilistic perceptual maps with implications for competitive positioning and choice

Abstract Perceptual product positioning maps which are derived from probabilistic scaling models possess some distinct advantages over their deterministic counterparts. However, many probabilistic models still labor under a number of restrictive mathematical conditions. This paper describes an anisotropic space extension that alleviates some of these limitations by explicitly modeling the dimensional variances and covariances of each brand in a product positioning map. To clarify the decisions necessary when using probabilistic scaling models and to illustrate some of their attractive properties, two sets of convenience goods data are analyzed. The applications focus on the models implications for the understanding of brand positioning and choice probabilities.