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Katya Tentori - One of the best experts on this subject based on the ideXlab platform.
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What can the Conjunction Fallacy tell us about human reasoning?
2020Co-Authors: Katya TentoriAbstract:In this chapter, I will briefly summarize and discuss the main results obtained from more than three decades of studies on the Conjunction Fallacy (hereafter CF) and will argue that this striking and widely debated reasoning error is a robust phenomenon that can systematically affect laypeople’s as much as experts’ probabilistic inferences, with potentially relevant real-life consequences. I will then introduce what is, in my view, the best explanation for the CF and indicate how it allows the reconciliation of some classic probabilistic reasoning errors with the outstanding reasoning performances that humans have been shown capable of. Finally, I will tackle the open issue of the greater accuracy and reliability of evidential impact assessments over those of posterior probability and outline how further research on this topic might also contribute to the development of effective human-like computing.
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Noisy probability judgment, the Conjunction Fallacy, and rationality: Comment on Costello and Watts (2014).
Psychological review, 2016Co-Authors: Vincenzo Crupi, Katya TentoriAbstract:According to Costello and Watts (2014), probability theory can account for key findings in human judgment research provided that random noise is embedded in the model. We concur with a number of Costello and Watts's remarks, but challenge the empirical adequacy of their model in one of their key illustrations (the Conjunction Fallacy) on the basis of recent experimental findings. We also discuss how our argument bears on heuristic and rational thinking.
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Why quantum probability does not explain the Conjunction Fallacy.
The Behavioral and brain sciences, 2013Co-Authors: Katya Tentori, Vincenzo CrupiAbstract:We agree with Pothos & Busemeyer (P&B) that formal tools can be fruitfully employed to model human judgment under uncertainty, including well-known departures from principles of classical probability. However, existing findings either contradict P&B's quantum probability approach or support it to a limited extent. The Conjunction Fallacy serves as a key illustration of both kinds of problems.
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On the Determinants of the Conjunction Fallacy: Probability Versus Inductive Confirmation
Journal of experimental psychology. General, 2012Co-Authors: Katya Tentori, Vincenzo Crupi, S RussoAbstract:Major recent interpretations of the Conjunction Fallacy postulate that people assess the probability of a Conjunction according to (non-normative) averaging rules as applied to the constituents’ probabilities or represent the Conjunction Fallacy as an effect of random error in the judgment process. In the present contribution, we contrast such accounts with a different reading of the phenomenon based on the notion of inductive confirmation as defined by contemporary Bayesian theorists. Averaging rule hypotheses along with the random error model and many other existing proposals are shown to all imply that Conjunction Fallacy rates would rise as the perceived probability of the added conjunct does. By contrast, our account predicts that the Conjunction Fallacy depends on the added conjunct being perceived as inductively confirmed. Four studies are reported in which the judged probability versus confirmation of the added conjunct have been systematically manipulated and dissociated. The results consistently favor a confirmation–theoretic account of the Conjunction Fallacy against competing views. Our proposal is also discussed in connection with related issues in the study of human inductive reasoning.
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How the Conjunction Fallacy is tied to probabilistic confirmation: Some remarks on Schupbach (2009)
Synthese, 2012Co-Authors: Katya Tentori, Vincenzo CrupiAbstract:Crupi et al. (Think Reason 14:182–199, 2008) have recently advocated and partially worked out an account of the Conjunction Fallacy phenomenon based on the Bayesian notion of confirmation. In response, Schupbach (2009) presented a critical discussion as following from some novel experimental results. After providing a brief restatement and clarification of the meaning and scope of our original proposal, we will outline Schupbach’s results and discuss his interpretation thereof arguing that they do not actually undermine our point of view if properly construed. Finally, we will foster such a claim by means of some novel data.
Emmanuel M. Pothos - One of the best experts on this subject based on the ideXlab platform.
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Corrigendum: Is there a Conjunction Fallacy in legal probabilistic decision making? [Front. Psychol. 9, 391 (2018)] doi: 10.3389/fpsyg.2018.00391
Frontiers in Psychology, 2018Co-Authors: Bartosz Wojciechowski, Emmanuel M. PothosAbstract:© 2018 Wojciechowski and Pothos. Is There a Conjunction Fallacy in Legal Probabilistic Making? by Wojciechowski, B. W., and Pothos, E. M. (2018). Front. Psychol. 9:391. doi: 10.3389/fpsyg.2018.00391 In the original article, there was an error. In the Discussion section, a small error was made in one of the quantum computations, which requires minor adjustment of the discussion. None of the empirical results, analyses, and other conclusions are affected. A correction has been made to Discussion, paragraph 7. The original sentence was: For a double CF, we have: Prob(A), Prob(B) > Prob(A & B), that is a CF occurs for both conjuncts. This has been corrected to: For a double CF, we have: Prob(A), Prob(B) Prob(A & B), for when evaluating criminal cases for which the suspect was guilty for both crimes. This has been corrected to: For the participants with no legal background, we have a situation where Prob(A), Prob(B) < Prob(A & B), for when evaluating criminal cases for which the suspect was guilty for both crimes.
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corrigendum is there a Conjunction Fallacy in legal probabilistic decision making front psychol 9 391 2018 doi 10 3389 fpsyg 2018 00391
Frontiers in Psychology, 2018Co-Authors: Bartosz Wojciechowski, Emmanuel M. PothosAbstract:© 2018 Wojciechowski and Pothos. Is There a Conjunction Fallacy in Legal Probabilistic Making? by Wojciechowski, B. W., and Pothos, E. M. (2018). Front. Psychol. 9:391. doi: 10.3389/fpsyg.2018.00391 In the original article, there was an error. In the Discussion section, a small error was made in one of the quantum computations, which requires minor adjustment of the discussion. None of the empirical results, analyses, and other conclusions are affected. A correction has been made to Discussion, paragraph 7. The original sentence was: For a double CF, we have: Prob(A), Prob(B) > Prob(A & B), that is a CF occurs for both conjuncts. This has been corrected to: For a double CF, we have: Prob(A), Prob(B) Prob(A & B), for when evaluating criminal cases for which the suspect was guilty for both crimes. This has been corrected to: For the participants with no legal background, we have a situation where Prob(A), Prob(B) < Prob(A & B), for when evaluating criminal cases for which the suspect was guilty for both crimes.
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Is There a Conjunction Fallacy in Legal Probabilistic Decision Making
Frontiers in psychology, 2018Co-Authors: Bartosz Wojciechowski, Emmanuel M. PothosAbstract:Classical probability theory (CPT) has represented the rational standard for decision making in human cognition. Even though CPT has provided many descriptively excellent decision models, there have also been some empirical results persistently problematic for CPT accounts. The tension between the normative prescription of CPT and human behavior is particularly acute in cases where we have higher expectations for rational decisions. One such case concerns legal decision making from legal experts, such as attorneys and prosecutors and, more so, judges. In the present research we explore one of the most influential CPT decision fallacies, the Conjunction Fallacy (CF), in a legal decision making task, involving assessing evidence that the same suspect had committed two separate crimes. The information for the two crimes was presented consecutively. Each participant was asked to provide individual ratings for the two crimes in some cases and conjunctive probability rating for both crimes in other cases, after all information had been presented. Overall, 360 probability ratings for guilt were collected from 120 participants, comprised of 40 judges, 40 attorneys and prosecutors, and 40 individuals without legal education. Our results provide evidence for a double Conjunction Fallacy (in this case, a higher probability of committing both crimes than the probability of committing either crime individually), in the group of individuals without legal education. These results are discussed in terms of their applied implications and in relation to a recent framework for understanding such results, quantum probability theory (QPT).
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The Conjunction Fallacy, confirmation, and quantum theory: comment on Tentori, Crupi, and Russo (2013)
Journal of experimental psychology. General, 2015Co-Authors: Jerome R. Busemeyer, Zheng Wang, Emmanuel M. Pothos, Jennifer S. TruebloodAbstract: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 (QP) 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) presented an alternative account of the Conjunction Fallacy based on the concept of inductive confirmation. They presented new empirical findings consistent with their account, and they also claimed that these results were inconsistent with the QP theory account. This comment proved that our QP model for the Conjunction Fallacy is completely consistent with the main empirical results from Tentori et al. (2013). Furthermore, we discuss experimental tests that can distinguish the 2 alternative accounts.
Vincenzo Crupi - One of the best experts on this subject based on the ideXlab platform.
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Noisy probability judgment, the Conjunction Fallacy, and rationality: Comment on Costello and Watts (2014).
Psychological review, 2016Co-Authors: Vincenzo Crupi, Katya TentoriAbstract:According to Costello and Watts (2014), probability theory can account for key findings in human judgment research provided that random noise is embedded in the model. We concur with a number of Costello and Watts's remarks, but challenge the empirical adequacy of their model in one of their key illustrations (the Conjunction Fallacy) on the basis of recent experimental findings. We also discuss how our argument bears on heuristic and rational thinking.
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Why quantum probability does not explain the Conjunction Fallacy.
The Behavioral and brain sciences, 2013Co-Authors: Katya Tentori, Vincenzo CrupiAbstract:We agree with Pothos & Busemeyer (P&B) that formal tools can be fruitfully employed to model human judgment under uncertainty, including well-known departures from principles of classical probability. However, existing findings either contradict P&B's quantum probability approach or support it to a limited extent. The Conjunction Fallacy serves as a key illustration of both kinds of problems.
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On the Determinants of the Conjunction Fallacy: Probability Versus Inductive Confirmation
Journal of experimental psychology. General, 2012Co-Authors: Katya Tentori, Vincenzo Crupi, S RussoAbstract:Major recent interpretations of the Conjunction Fallacy postulate that people assess the probability of a Conjunction according to (non-normative) averaging rules as applied to the constituents’ probabilities or represent the Conjunction Fallacy as an effect of random error in the judgment process. In the present contribution, we contrast such accounts with a different reading of the phenomenon based on the notion of inductive confirmation as defined by contemporary Bayesian theorists. Averaging rule hypotheses along with the random error model and many other existing proposals are shown to all imply that Conjunction Fallacy rates would rise as the perceived probability of the added conjunct does. By contrast, our account predicts that the Conjunction Fallacy depends on the added conjunct being perceived as inductively confirmed. Four studies are reported in which the judged probability versus confirmation of the added conjunct have been systematically manipulated and dissociated. The results consistently favor a confirmation–theoretic account of the Conjunction Fallacy against competing views. Our proposal is also discussed in connection with related issues in the study of human inductive reasoning.
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How the Conjunction Fallacy is tied to probabilistic confirmation: Some remarks on Schupbach (2009)
Synthese, 2012Co-Authors: Katya Tentori, Vincenzo CrupiAbstract:Crupi et al. (Think Reason 14:182–199, 2008) have recently advocated and partially worked out an account of the Conjunction Fallacy phenomenon based on the Bayesian notion of confirmation. In response, Schupbach (2009) presented a critical discussion as following from some novel experimental results. After providing a brief restatement and clarification of the meaning and scope of our original proposal, we will outline Schupbach’s results and discuss his interpretation thereof arguing that they do not actually undermine our point of view if properly construed. Finally, we will foster such a claim by means of some novel data.
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On the Conjunction Fallacy and the meaning of and, yet again: a reply to Hertwig, Benz, and Krauss (2008).
Cognition, 2011Co-Authors: Katya Tentori, Vincenzo CrupiAbstract:Abstract In 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 Fallacy should be instead considered as reflecting “reasonable pragmatic and semantic inferences” because the meaning of and does not always coincide with that of the logical operator ∧ . We also question the relevance of the experimental evidence that HBK provide in support of their argument as well as their account of the pertinent literature. Finally, we report two novel experiments in which we employed HBK’s procedure to control for the interpretation of and. The results obtained overtly contradict HBK’s data and claims. We conclude with a discussion on the alleged feebleness of the Conjunction Fallacy, and suggest directions that future research on this topic might pursue.
Fintan Costello - One of the best experts on this subject based on the ideXlab platform.
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Explaining High Conjunction Fallacy Rates: The Probability Theory Plus Noise Account
Journal of Behavioral Decision Making, 2016Co-Authors: Fintan Costello, Paul WattsAbstract:The Conjunction Fallacy occurs when people judge the conjunctive probability P(A ∧ B) to be greater than a constituent probability P(A), contrary to the norms of probability theory. This Fallacy is a reliable, consistent and systematic part of people's probability judgements, attested in many studies over at least 40 years. For some events, these fallacies occur very frequently in people's judgements (at rates of 80% or more), while for other events, the fallacies are very rare (occurring at rates of 10% or less). This wide range of Fallacy rates presents a challenge for current theories of the Conjunction Fallacy. We show how this wide range of observed Fallacy rates can be explained by a simple model where people reason according to probability theory but are subject to random noise in the reasoning process. Copyright © 2016 John Wiley & Sons, Ltd.
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How probability theory explains the Conjunction Fallacy
Journal of Behavioral Decision Making, 2009Co-Authors: Fintan CostelloAbstract:The Conjunction Fallacy occurs when people judge a conjunctive statement B-and-A to be more probable than a constituent B, in contrast to the law of probability that P(B ∧ A) cannot exceed P(B) or P(A). Researchers see this Fallacy as demonstrating that people do not follow probability theory when judging conjunctive probability. This paper shows that the Conjunction Fallacy can be explained by the standard probability theory equation for Conjunction if we assume random variation in the constituent probabilities used in that equation. The mathematical structure of this equation is such that random variation will be most likely to produce the Fallacy when one constituent has high probability and the other low, when there is positive conditional support between the constituents, when there are two rather than three constituents, and when people rank probabilities rather than give numerical estimates. The Conjunction Fallacy has been found to occur most frequently in exactly these situations. Copyright © 2008 John Wiley & Sons, Ltd.
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Fallacies in probability judgments for Conjunctions and disjunctions of everyday events
Journal of Behavioral Decision Making, 2009Co-Authors: Fintan CostelloAbstract:The Conjunction Fallacy occurs when people judge a Conjunction B-and-A as more probable than a constituent B, contrary to probability theory's ‘Conjunction rule’ that a Conjunction cannot be more probable than either constituent. Many studies have demonstrated this Fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the Conjunction rule is not a Fallacy. This paper describes three experiments showing that the Conjunction Fallacy occurs as consistently for Conjunctions where frequentist probability theory is valid (Conjunctions of everyday weather events) as for other Conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the Conjunction Fallacy and the disjunction Fallacy (which arises when a disjunction B-or-A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.
Nicholas Frank Pidgeon - One of the best experts on this subject based on the ideXlab platform.
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Conditional Probabilities, Potential Surprise, and the Conjunction Fallacy
The Quarterly Journal of Experimental Psychology Section A, 1998Co-Authors: John E. Fisk, Nicholas Frank PidgeonAbstract:Tversky and Kahneman (1983) found that a relationship of positive conditional dependence between the components of a Conjunction of two events increases the prevalence of the Conjunction Fallacy. Consistent with this finding, the results of two experiments reveal that dependence leads to higher estimates for the conjunctive probability and a higher incidence of the Fallacy. However, contrary to the theoretical account proposed by Tversky and Kahneman, the actual magnitude of the conditional relationship does not directly affect the extent of the Fallacy; all that is necessary is for a positive conditional relationship to exist. The pattern of results obtained can be accounted for in terms of Shackle's (1969) “potential surprise” theory of subjective probability. Surprise theory predicts that the impact of the conditional event will be at its maximum where the relationship is a negative one. Tversky and Kahneman's model, on the other hand, predicts the maximum effect when the relationship is positive. In a...
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The Conjunction Fallacy: The case for the existence of competing heuristic strategies
British Journal of Psychology, 1997Co-Authors: John E. Fisk, Nicholas Frank PidgeonAbstract:A study was conducted to evaluate the effects of training on the incidence of the Conjunction Fallacy. One group received training in the extension rule (normative), the other training which stressed that judgments should be based on similarity or representativeness (non-normative). Participants receiving the former made fewer errors, those receiving the latter made more errors. However, multiple regression analysis showed that under both training regimes in a majority of instances only the smaller component probability was statistically significant in determining the Conjunction. A second study, omitting the training element, replicated this finding. Both studies highlight the fact that existing theories cannot account for the pattern of participants' responses under the training conditions employed. It is proposed that rather than choose between two competing strategies (Agnoli & Krantz, 1989), participants derive their estimate in two stages, first by selecting a reference point in the probability continuum, usually based on the ‘ surprise value’ of the smaller component event (Shackle, 1969) and then assigning a value to the Conjunction relative to this point. During the second stage, training is hypothesized to produce its effect as participants weigh the available information deriving some compromise reflecting both normative and non-normative tendencies.
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Component probabilities and the Conjunction Fallacy: Resolving signed summation and the low component model in a contingent approach
Acta Psychologica, 1996Co-Authors: John E. Fisk, Nicholas Frank PidgeonAbstract:This study investigates the conflicting implications of the low component and signed summation explanations for the Conjunction Fallacy. Error data across three different Conjunction types replicate the pattern found by Yates and Carlson (1986), but the results also reveal, consistent with the predictions of the low component model, that for Conjunctions of an unlikely event with a likely event (LU) the unlikely component is given disproportionate weight by subjects. However, this result did not generalise to Conjunctions of an unlikely with an unlikely event (UU), nor to those involving a likely with a likely (LL). The combined results show the Conjunction Fallacy is highly sensitive to task characteristics, and suggests the need for a more contingent explanation of the phenomenon. We argue that the low component model and signed summation are both compatible within a process-based explanation that distinguishes between problem structuring and Conjunction evaluation.