Preference and similarity between alternatives

We discuss how information about choice-relevant differences between alternatives can be revealed from preference information. We provide axiomatic characterisations of two classes of Similarity Revelation Rules: one that allows for different similarity thresholds for different pairs of alternatives, and one in which the threshold is the same for all pairs of alternatives. A third result proves the necessary and sufficient condition for the characterised class of rules to yield a transitive similarity relation. The article concludes with a discussion of the limitations of the analysis and the relationship between transitivity (of preferences) and the choice-relevant similarities between options.