The conjunction fallacy, confirmation, and quantum theory: Comment on Tentori, Crupi, and Russo (2013).

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Copyright and reuse: City Research Online aims to make research outputs of City, University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to. City Research Online: http://openaccess.city.ac.uk/ publications@city.ac.uk Permanent repository link: City Research OnlineThe conjunction fallacy, confirmation, and quantum theory: comment on Tentori, Crupi, & Russo (2013) Jerome R. BusemeyerIndiana University Zheng WangThe Ohio State University Emmanuel M. Pothos City University LondonJennifer S. Trueblood University of California, IrvineAbstract The conjunction fallacy refers to situations when a person judges a conjunction to be more likely than one of the individual conjuncts, which is a violation of a key property of classical probability theory. Recently, quantum probability theory has been proposed as a coherent account of these and many other findings on probability judgment "errors" that violate classical probability rules, including the conjunction fallacy. Tentori, Crupi, and Russo (2013) present an alternative account of the conjunction fallacy based on the concept of inductive confirmation. They present new empirical findings consistent with their account, and they also claim that these results are inconsistent with the quantum probability theory account. This comment proves that our quantum probability model for the conjunction fallacy is completely consistent with the main empirical results from . Furthermore, we discuss experimental tests that can distinguish the two alternative accounts.This comment concerns a recent debate over formal explanations for the conjunction fallacy (Tversky & Kahneman, 1983). This fallacy occurs when a person judges the likelihood of the conjunctive event (A and B) to be greater than the likelihood of one of the events, say A, alone. The most well-known example is about a hypothetical person, Linda (L), who is described in a way that she looks very much like a feminist (F ) and not at all like a bank QUANTUM CONJUNCTION 2 teller (B ). Participants are asked to rank order the relative likelihood of various statements about Linda, including the statement that "Linda is a bank teller" (B ) and that "Linda is a feminist and a bank teller" (F and B ). Participants typically order the (F and B ) event as more likely than the B event. There is an impressive amount of research replicating and extending this finding, which establishes its robustness (for a review, see , hereafter referred to as TCR). Of course, the conjunction fallacy does not occur all the time, and establishing when it does occur is a critical question. This question was recently addressed by TCR, who put forth an argument that inductive confirmation (IC) rather than perceived probability (PP), described below, is a key determinant. TCR provide strong empiric...

Quantum-like models cannot account for the conjunction fallacy

“…Overall, our result is in line with previous suggestions that degenerate models should be preferred to non-degenerate models, as the latter should be considered as "toy models" only (e.g. Busemeyer and Bruza 2012;Busemeyer et al 2015). The second research hypothesis extends the first one by considering also degenerate models, that is, models in which an answer is represented by a N -D subspace, e.g.…”

“…Consequently, the corresponding probabilities of answering "yes" to questions Q B and Q F depend on the order of presentation of the questions: it is an order effect More importantly, it can be shown that only models that display an order effect are able to account for the conjunction fallacy (cf. Busemeyer et al 2011Busemeyer et al , 2015Busemeyer and Bruza 2012;Bruza et al 2015, p. 388). In other words, the quantumlike models of Sect.…”

Une nouvelle approche expérimentale pour tester les modèles quantiques de l’erreur de conjonction

“…Les résultats expérimentaux que nous avons obtenus, s'ils ne permettent pas d'exclure les modèles quantiques de façon générale, montrent nettement que leséquations GR ne sont pas vérifiées, et donc que ces modèles quantiques non-dégénérés ne sont pas adéquats d'un point de vue empirique, et ne peuvent pré-tendre rendre compte de l'erreur de conjonction pour les 4 histoires considérées. Ceci confirme certaines intuitions de la littérature (e. g. Busemeyer et al 2015) selon lesquelles les modèles non-dégénérés doivent surtout avoir un rôle illustratif. Nous avons considéré ici des histoires variées, appartenant aux deux types d'erreur de conjonction distingués (AB et MA), ce qui suggère fortement que les erreurs de conjonction en général ne sont pas explicables par des modèles quantiques non-dégénérés.…”

“…Pourêtre légitime, une explication doit reposer sur des modèles empiriquement adéquats. Aussi, nous poursuivrons ici l'étude de l'adéquation empirique de ces modèles quantiques, dans la lignée de travaux ré-cents (e. g. , Pothos et Busemeyer 2013, Busemeyer et al 2015, Boyer-Kassem et al 2016. L'originalité de notreétude consistè a avoir conçu et realisé un protocole experimental qui permet d'observer l'erreur de conjonction comme un effet résultant d'un autre biais cognitif (l'effet d'ordre).…”

“…Les modèles les plus simples, dits « non-dégénérés », peuvent-ilsêtre suffisants, ou des modèles plus complexes, avec un nombre plus grand de dimensions et dits « dégénérés », sont-ils requis ? La littérature existante est plutôt favorable aux modèles dégénérés car le grand nombre de dimensions devrait permettre de mieux représenter la complexité du processus cognitif, et elle a tendanceà considérer les modèles non-dégénérés comme des modèles seulement illustratifs (Busemeyer et al 2015). Cependant, le choix entre les deux types de modèles n'a pasété définitivement arrêté.…”