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A quantum geometric model of similarity

Pothos, E. M., Busemeyer, J. R. and Trueblood, J. S. (2013). A quantum geometric model of similarity. Psychological Review, 120(3), pp. 679-696. doi: 10.1037/a0033142

Abstract

No other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality, and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tversky’s (1997) main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general.

Publication Type: Article
Additional Information: This version is the author's pre-print, posted 16/04/2013, and has not been published yet. Therefore, this article may not exactly replicate the final version published in the APA journal. It is not the copy of record.
Publisher Keywords: similarity, metric axioms, symmetry, triangle inequality, diagnosticity, quantum probability
Subjects: B Philosophy. Psychology. Religion > BF Psychology
Departments: School of Arts & Social Sciences > Psychology
URI: http://openaccess.city.ac.uk/id/eprint/2250
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