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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...