Imperfect discrimination, similarity, and stochastic transitivity

Daniele Caliari ()
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Daniele Caliari: WZB—Berlin Social Science Center

Economic Theory Bulletin, 2024, vol. 12, issue 2, No 7, 199-209

Abstract: Abstract We study the relationship between imperfect discrimination, similarity, and stochastic transitivity in generalized versions of Perturbed Utility (Fudenberg et al. in Econometrica 83(6):2371–2409, 2015) and Fechnerian models (Debreu in Econometrica 26(3):440–444, 1958). We show that these models are equivalent and that, within them, the properties of a similarity function can characterize all notions of stochastic transitivity (as Weak, Moderate, and Strong). Specifically, He and Natenzon (Am Econ Rev Insights 6(2):176–195, 2024) have recently shown that choice probabilities are moderately transitive if and only if the similarity function is a metric. We provide a counterpoint and show that unless choice probabilities are strongly transitive, the similarity function can violate the triangle inequality.

Keywords: Stochastic choice; Imperfect discrimination; Perturbed utility & Fechnerian models; Similarity hypothesis (search for similar items in EconPapers)
JEL-codes: D0 D9 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40505-024-00273-x

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