On the determinants of the conjunction fallacy: Probability versus inductive confirmation.

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...

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“…The conjunction fallacy, confirmation, and quantum theory: comment on Tentori, Crupi, & Russo (2013) Jerome R. Busemeyer…”

Section: City Research Onlinementioning

confidence: 99%

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

Busemeyer¹,

Wang²,

Pothos³

et al. 2015

Journal of Experimental Psychology: General

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“…First, people often combine the constituent probabilities as a configural weighted average (Gavanski and Roskos-Ewoldsen, 1991; Nilsson, 2008; Nilsson et al, 2009; Jenny et al, 2014). Second, the rate of conjunction fallacies is mediated by the inductive confirmation for the conjunction (Tentori et al, 2013). The effect is thus affected by the believability of the conjunctive event (Kahneman and Tversky, 1982; Tentori et al, 2013) with the rate of fallacies dropping if the conjunctions include contradictory conjuncts such as “Alan is bored with music” and “Alan plays Jazz for a hobby.” It is moreover often assumed that the responses are negotiated by two cognitive systems.…”

Section: Correspondence and Coherence Of Probability Judgmentsmentioning

confidence: 99%

“…Second, the rate of conjunction fallacies is mediated by the inductive confirmation for the conjunction (Tentori et al, 2013). The effect is thus affected by the believability of the conjunctive event (Kahneman and Tversky, 1982; Tentori et al, 2013) with the rate of fallacies dropping if the conjunctions include contradictory conjuncts such as “Alan is bored with music” and “Alan plays Jazz for a hobby.” It is moreover often assumed that the responses are negotiated by two cognitive systems. An intuitive system that tends to produce conjunction fallacies that is (imperfectly) monitored by an analytic system with some insight about the rules of probability theory (Kahneman and Frederick, 2002; Peters et al, 2006; Evans, 2008), where the latter is partially tapped by numeracy (Liberali et al, 2012).…”

Section: Correspondence and Coherence Of Probability Judgmentsmentioning

confidence: 99%

The role of ANS acuity and numeracy for the calibration and the coherence of subjective probability judgments

et al. 2014

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The purpose of the study was to investigate how numeracy and acuity of the approximate number system (ANS) relate to the calibration and coherence of probability judgments. Based on the literature on number cognition, a first hypothesis was that those with lower numeracy would maintain a less linear use of the probability scale, contributing to overconfidence and nonlinear calibration curves. A second hypothesis was that also poorer acuity of the ANS would be associated with overconfidence and non-linearity. A third hypothesis, in line with dual-systems theory (e.g., Kahneman and Frederick, 2002) was that people higher in numeracy should have better access to the normative probability rules, allowing them to decrease the rate of conjunction fallacies. Data from 213 participants sampled from the Swedish population showed that: (i) in line with the first hypothesis, overconfidence and the linearity of the calibration curves were related to numeracy, where people higher in numeracy were well calibrated with zero overconfidence. (ii) ANS was not associated with overconfidence and non-linearity, disconfirming the second hypothesis. (iii) The rate of conjunction fallacies was slightly, but to a statistically significant degree decreased by numeracy, but still high at all numeracy levels. An unexpected finding was that participants with better ANS acuity gave more realistic estimates of their performance relative to others.

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“…These effects are appropriately measured by the Bayesian distinction between argument strength, the degree of belief bought about by an argument, and argument force, which can be measured by the likelihood ratio. Argument force has also been appealed to in accounting for the conjunction fallacy (Tentori, Crupi, & Russo, 2013) and Rips (2001, p. 129, foonote 1) has also argued for the importance of an appropriate measure of change between prior and posterior. In our explanatory model, this is the quantity indexed by β 1 .…”

Section: Discussionmentioning

confidence: 99%

Discounting testimony with the argument ad hominem and a Bayesian congruent prior model.

Bhatia

Oaksford

2015

Journal of Experimental Psychology: Learning, Memory, and Cogni

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When directed to ignore evidence of a witness' previous bad character because of a violation of the rules of evidence, are jurors' beliefs still affected? The intuition is that they will be because in everyday argumentation, fallacies, like the ad hominem, are effective argumentative strategies. An ad hominem argument (against the person) undermines a conclusion by questioning the character of the proposer. This intuition divides current theories of argumentation. According to pragmadialectical theory (e.g., Van Eemeren & Grootendorst, 2004) procedural rules exactly like the rules of evidence are part of our cognitive resources for evaluating arguments. If one of these rules is violated, an argument should be treated as a fallacy and so it should not alter someone's belief in the conclusion.Some recent experiments investigating how reasonable these arguments are perceived to be seem to support this account (Van Eemeren, Garssen, & Meufells, 2009). These experiments are critiqued from the perspective of the relevance (Walton, 2008(Walton, , 2009) and epistemic (Hahn & Oaksford, 2006Oaksford & Hahn, 2004) approaches to argumentation. An experiment investigates the predictions of these approaches for a graded belief change version of Van Eemeren et al.'s (2009) experiment and the results are modelled using a Bayesian congruent prior model. These results cannot be explained by the pragmadialectical approach and show that in everyday argument people are extremely sensitive to the epistemic relevance of evidence. Moreover, it seems highly unlikely that this can be switched off in more formal contexts such as the courtroom. In the court room, many factors affect how persuasive jurors find the arguments put forward by counsel (Spellman & Schauer, 2012). The arguments presented in court are constrained by strict procedural rules about, for example, admissible evidence, not asking leading questions and so on. These procedural rules guarantee the quality of the arguments and evidence.However, lawyers occasionally violate these rules, intentionally or unintentionally, in order to influence the jury. For example, counsel may introduce evidence of a witness' previous bad character, e.g., media reports of drunkenness or wife abuse. In In the US, under the Federal Rules of Evidence (2014) this may be inadmissible as irrelevant hearsay but only if the opposing counsel objects will the judge rule on its admissibility. At this point, she can inform the jury that the rules of evidence have been violated and direct them to ignore the evidence.The goal of the arguments put forward in court is to bring about quantitative changes in jurors' degrees of belief, ultimately, in the guilt or innocence of the defendant. When the judge points out that an argument, e.g., the witness abused his wife, violates a rule of evidence does this affect jurors' degrees of belief in the conclusions they are asked to evaluate? Pointing out the violation is intended to remove any effect of the argument on jurors' degree of belief but once it has...

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On the determinants of the conjunction fallacy: Probability versus inductive confirmation.

Cited by 132 publications

References 83 publications

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

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

The role of ANS acuity and numeracy for the calibration and the coherence of subjective probability judgments

Discounting testimony with the argument ad hominem and a Bayesian congruent prior model.

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