Crupi, Vincenzo

Tentori, K

English

Institutional Research Information System University of Turin

On the conjunction fallacy and the meaning of and, yet again:A reply to Hertwig, Benz, and Krauss (2008)Katya Tentori a,⇑, Vincenzo Crupi b,caDiSCoF, CIMeC, University of Trento, corso Bettini 31, 38068 Rovereto, ItalybDepartment of Philosophy, University of Turin, via S. Ottavio 20, 10124 Turin, ItalycMunich Center for Mathematical Philosophy, Ludwig Maximilian University, Ludwigstrasse 31, D-80539 München, Germanya r t i c l e i n f oArticle history:Received 25 July 2010Revised 9 September 2011Accepted 14 September 2011Available online 12 November 2011Keywords:Conjunction fallacyPragmatic inferencesProbabilistic reasoninga b s t r a c tIn this paper we question the theoretical tenability of Hertwig, Benz, and Krauss’s (2008)(HBK) argument that responses commonly taken as manifestations of the conjunction fal-lacy should be instead considered as reflecting ‘‘reasonable pragmatic and semantic infer-ences’’ because the meaning of and does not always coincide with that of the logicaloperator ^. We also question the relevance of the experimental evidence that HBK providein support of their argument as well as their account of the pertinent literature. Finally, wereport two novel experiments in which we employed HBK’s procedure to control for theinterpretation of and. The results obtained overtly contradict HBK’s data and claims. Weconclude with a discussion on the alleged feebleness of the conjunction fallacy, and suggestdirections that future research on this topic might pursue.! 2011 Elsevier B.V. All rights reserved.1. IntroductionSince the early Eighties, about a hundred scientific pa-pers on the conjunction fallacy (CF) have been published.Such wide interest is easy to understand, as the CF has be-come a key topic in the fervent debate on human rational-ity. Indeed, from the very beginning the CF phenomenonhas been described as a violation of ‘‘the simplest and themost basic qualitative law of probability’’ (Tversky & Kahn-eman, 1983, p. 293; but already mentioned in Tversky &Kahneman, 1982, p. 90). The law at issue is the conjunctionrule, a principle whose compelling nature appearsunequivocal when stated formally: Pr(p ^ q) 6 Pr(p), i.e.,the joint occurrence of a pair of events (p and q) cannotbe more probable than the occurrence of anyone of them(e.g., p).In contrast, what does seem surprising across morethan 30 years of research is the recurrence of questionsabout the validity of CF experiments. A standard line ofargument inspired by the pragmatics of communicationhas been that violation of the conjunction rule need notbe irrational if it results from interpreting the experimentaltask in ways that rob it of normative relevance. The mainsources of misinterpretation considered in the literatureinclude participants’ understanding of the isolated con-junct p, the term probable, and the connective and. Manytechniques have been developed to control for each ofthese possible misinterpretations (see Moro, 2009, for a re-cent review), but none of them has dissipated the effect.Nonetheless some concerns turned out to be importantand should be credited for having fostered improvementsin the experimental procedures by which the CF is investi-gated. To illustrate, the suspicion that the single conjunct pmight be interpreted as p-and-not-q (Adler, 1984; Dulany& Hilton, 1991; Messer & Griggs, 1993; Morier & Borgida,1984; Polizer & Noveck, 1991; but already discussed inTversky and Kahneman, 1982, 1983) led to more carefulcontrol of stimuli, such as explicitly including the state-ment p-and-not-q in the judgment task along with p andp-and-q. When this technique is applied (as in Tentori,Bonini, & Osherson, 2004; Wedell & Moro, 2008), the rate0010-0277/$ - see front matter ! 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.cognition.2011.09.002⇑ Corresponding author.E-mail address: katya.tentori@unitn.it (K. Tentori).Cognition 122 (2012) 123–134Contents lists available at SciVerse ScienceDirectCognitionjournal homepage: www.elsevier .com/locate /COGNIT

On the conjunction fallacy and the meaning of and, yet again: A reply to Hertwig, Benz, and Krauss

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On the conjunction fallacy and the meaning of and, yet again: A reply to Hertwig, Benz, and Krauss

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