A Theoretical Investigation of the Effects of Similarity on Brand Choice Using the Elimination-by-Tree Model

IIA (independence of irrelevant alternatives) axiom states that the ratio of choice probabilities of any two brands will depend only on the utilities of the brands. However, even if the utilities of brands are assumed to be fixed, their choice probabilities will be affected by the similarity between them. This study and several other previous studies show that a more preferred (higher utility) brand benefits more in a high similarity situation than a less preferred (lower utility) brand, which is called the asymmetric similarity effect or simply the asymmetric effect in this study. This study expands on the asymmetric effect that has been reported by many previous empirical studies and implied in choice modeling literature, by giving it an explicit mathematical formulation based on the analysis of the elimination-by-tree (EBT) model (Tversky and Sattath 1979). This study also provides an integrative theoretical summary showing how the asymmetric effect is related to the similarity effect, dominance effect, and IIA condition.