Frequency illusions and other fallacies

Sloman, Steven A.; Over, David E.; Slovak, Lila; Stibel, Jeffrey M.

doi:10.1016/s0749-5978(03)00021-9

Cited by 198 publications

(229 citation statements)

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“…The current Experiment 1 and the observation that about a quarter of people arrived at a union reading (see the Venn diagram task) suggest that the large difference in violations of the conjunction rule between Hertwig's (1995) two frequency representations may partly be due to the ambiguity of the and connective and partly be owed to the difference in response mode (ranking versus estimation). In fact, Sloman et al (2003) found -using a who connective -that 69.9% participants violated the conjunction rule in a frequency ranking, relative to 33.3% in a frequency estimation version of the Linda task (for similar findings see also Wedell & Moro, 2008).…”

Section: (50)mentioning

confidence: 76%

“…narrows down the spectrum of possible interpretations to meanings that follow mathematical probability. In contrast, Kahneman and Tversky (1996) and Sloman, Over, Slovak, and Stibel (2003) have argued that the frequency effect results from the impact of extensional cues that are more salient in frequency formats.…”

Section: (50)mentioning

confidence: 94%

“…Sloman et al (2003) suggested that ''ranking would lead to more conjunction errors, because it forces a choice between the critical statements" (p. 306). Therefore, some people may violate the conjunction rule when they are forced to choose between two alternatives that they consider equally probable (frequent).…”

Section: (50)mentioning

confidence: 99%

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The conjunction fallacy and the many meanings of and

2008

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a b s t r a c tAccording to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator^, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language ''and" can convey a wide range of relationships between conjuncts such as temporal order (''I went to the store and bought some whisky"), causal relationships (''Smile and the world smiles with you"), and can indicate a collection of sets rather than their intersection (as in ''He invited friends and colleagues to the party"). When ''and" is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator^, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people's understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator^. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.Ó 2008 Elsevier B.V. All rights reserved.. . .it is a mistake to analyze natural language words like and as being identical to entities of the man-made logical terminology which so clearly derives from natural language (rather than the other way around) and so clearly has needs and purposes distinct from those of natural language (Sweetser, 1990, p. 92).One of the most frequent words in the English language is and. In Leech, Rayson, and Wilson's (2001) analysis of word frequencies in a 100 million word collection of samples of written and spoken language (the British National Corpus) the unremarkable three-letter word ''and" is the third most frequent word. Its commonness and plainness, however, do not mean that the most general connective in the English language lacks the ability to convey a wide range of relationships between the states of affairs described by the conjuncts. In fact, one reason for linguists' enduring fascination with and is that among all coordinating conjunctions (e.g., or, but, nor) it has the least semantic and syntactic limits, the least specific meaning, and the highest context dependency (Lang, 1991).Take, for instance, the use of and in (1): (1) Her husband is in hospital and she is seeing other men.As Kitis (2000) pointed out, the and in (1) does much more than conjoin the two clauses. Rather, it functions as an ''emotional device" that communicates the speaker's emotional attitude, surprise, or even outrage.The notion of and's context dependency stands in stark contrast with the highly constrained meaning of the logical and operator (^). The logical^represents the Boolean intersection of two sets. For illustration, if set A contains all even numbers (mu...

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Section: (50)mentioning

confidence: 76%

Section: (50)mentioning

confidence: 94%

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The conjunction fallacy and the many meanings of and

2008

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“…These results suggest that failure to form a joint representation (which corresponds to incompatibility in QP theory) is the primary source of the conjunction fallacy (Sloman et al, 2003;Reyna & Brainerd, 2008).…”

Section: Empirically Distinguishing the Quantum Vs Confirmation Accomentioning

confidence: 93%

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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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 model theory predicts various phenomena, including the occurrence of systematic illusions. It also postulates that naïve individuals infer a conditional probability, p (B|A), not by using Bayes's rule, but by working out the subset of cases of A in which B holds (for experimental corroboration, see Girotto & Gonzalez, 2001Johnson-Laird et al, 1999; see also Evans, Handley, Perham, Over, & Thompson, 2000;Sloman, Over, Slovak, & Stiebel, 2003). The theory also predicts that naïve individuals, including children, can solve probability problems asking for a simple combinatorial analysis of possibilities (for experimental evidence, see Girotto & Gonzalez, in press-a, -b).…”

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The Probability of Conditionals

Girotto

Johnson‐Laird

2004

PSYCHOLOGIA -An International Journal of Psychological Sciences

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We report two studies investigating how naïve reasoners evaluate the probability that a conditional assertion is true, and the conditional probability that the consequent of the conditional is true given that the antecedent is true. The mental model theory predicts that individuals should evaluate the probability of a conditional on the basis of the mental models representing the conditional, and that evaluations calling for a greater number of models should be more difficult. It follows that the probability of a conditional should differ from the corresponding conditional probability. The results of the studies corroborated these predictions, and contrast with alternative accounts of naive evaluations of the probability of conditionals.

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Frequency illusions and other fallacies

Cited by 198 publications

References 28 publications

The conjunction fallacy and the many meanings of and

The conjunction fallacy and the many meanings of and

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

The Probability of Conditionals

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