The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

Villejoubert, Gaëlle; Mandel, David R.

doi:10.3758/bf03195278

Cited by 111 publications

(109 citation statements)

References 35 publications

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“…In case an apparent violation would be observed within-participant (for example, suppose that P participant (A∪B)>P participant (A)+P participant (B)), the experimenter should verify that A∩ B is assumed by the participants to be empty. Several within-participants studies show a possible violation of the complementarity constraint: Robinson and Hastie 1985, van Wallendael and Hastie 1990, Villejoubert and Mandel 2002, Windschitl 2000. However, in none of these studies did the experimenters verify whether their definition of the set of the possible alternative hypotheses coincided with that of the participants.…”

Section: Constraints Due To the Static Coherence Criterionmentioning

confidence: 99%

Is the mind Bayesian? The case for agnosticism

Baratgin

Politzer

2006

Mind & Society

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This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: An epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (i) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (ii) the notorious case of the null priors. In both cases Lewis' rule is an appropriate alternative to Bayes' rule, but its use faces the same operational difficulties.Keywords Probability judgment • Subjective Bayesianism • Bayesian coherence • Probability revising • Probability updating • Linguistic pragmatics 2 IntroductionIn the imposing literature devoted to the psychological study of probability judgment, the use of a theoretical model as a referential norm for "rational" behavior is a usual methodology.1 Since the pioneering study by Rouanet (1961), and following the famous article by Edwards et al. (1963), the Bayesian model of probability has been the most frequently used as a normative reference or as a possible descriptive model. The implicit question that these studies attempt to answer is whether human beings perform probability judgment in a "Bayesian" manner. These interrogations go far beyond the realm of psychology: They also apply to the various domains that use the Bayesian model, such as economics (Davis and Holt 1993), law (Callen 1982), medicine (Casscells et al. 1978), artificial intelligence (Cohen 1985) and philosophy (Stich 1990).The present paper is not directly aimed towards these important debates concerning probabilistic functioning in humans, but is rather a methodological examination of the conditions under which the Bayesian model may be used as a normative theory. In other words, it aims to find an answer to the following question: Does the psychological literature take into consideration the various implications and constraints imposed by the usage of the Bayesian model as a normative reference? It will be argued that the answer is negative, an...

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Section: Constraints Due To the Static Coherence Criterionmentioning

confidence: 99%

Is the mind Bayesian? The case for agnosticism

Baratgin

Politzer

2006

Mind & Society

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“…In our experiments, we used a modified version of the planet Vuma scenario, a words-and- Skov & Sherman, 1986;Slowiaczek et al, 1992;Villejoubert & Mandel, 2002). In particular, we used the standard probability format (i.e., percentages) to convey the distributions of Gloms and Fizos on Vuma as well as their feature distributions.…”

Section: Information Formatmentioning

confidence: 99%

“…We used a modified version of the planet Vuma scenario introduced by Skov and Sherman (1986) and thereafter widely used in the hypothesis-testing literature (Garcia-Marques, Sherman, & Palma-Oliveira, 2001;McKenzie, 2006;Nelson, 2005;Nelson et al, 2010;Rusconi & McKenzie, in press;Sacchi et al, 2012, Study 3;Slowiaczek et al, 1992;Villejoubert & Mandel, 2002). The prior probabilities of the hypotheses were set as not equiprobable to obtain divergent predictions from the OED models, which can lead to the same utility values when priors are equal (Nelson, 2005(Nelson, , 2008.…”

Section: Materials and Proceduresmentioning

confidence: 99%

“…There is a large Bayesian reasoning literature on how people evaluate evidence to make judgments (e.g., Beach, 1968;Cherubini, Rusconi, Russo, & Crippa, 2013;Cosmides & Tooby, 1996;Fischhoff & Beyth-Marom, 1983;Gigerenzer & Hoffrage, 1995;Hammerton, 1973;McKenzie, 1994;Rusconi, Crippa, Russo, & Cherubini, 2012;Rusconi, Marelli, Russo, D'Addario, & Cherubini, 2013;Rusconi & McKenzie, in press;Slovic & Lichtenstein, 1971;Villejoubert & Mandel, 2002). The issue of whether people's intuitions about the value of obtained evidence align with theoretically optimal models has been the object of recent studies that noted the theoretical and empirical validity of two norms, namely, measures L and Z (e.g., Crupi, Tentori, & Gonzalez, 2007;Fitelson, 2001Fitelson, , 2006Mastropasqua, Crupi, & Tentori, 2010;Tentori, Crupi, Bonini, & Osherson, 2007).…”

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Evidence evaluation: Measure Z corresponds to human utility judgments better than measure L and optimal-experimental-design models.

Rusconi¹,

Marelli²,

D’Addario³

et al. 2014

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Evidence evaluation is a crucial process in many human activities, spanning from medical diagnosis to impression formation. The present experiments investigated which, if any, normative model best conforms to people's intuition about the value of the obtained evidence. Psychologists, epistemologists, and philosophers of science have proposed several models to account for people's intuition about the utility of the obtained evidence with respect either to a focal hypothesis or to a constellation of hypotheses. We pitted against each other the so called optimal-experimental-design models (i.e., Bayesian diagnosticity, log 10 diagnosticity, information gain, Kullback-Leibler distance, probability gain, and impact) and measures L and Z to compare their ability to describe humans' intuition about the value of the obtained evidence. Participants received words-andnumbers scenarios concerning two hypotheses and binary features. They were asked to evaluate the utility of "yes" and "no" answers to questions about some features possessed in different proportions (i.e., the likelihoods) by two types of extraterrestrial creatures (corresponding to two mutually exclusive and exhaustive hypotheses). Participants evaluated either how an answer was helpful or how an answer decreased/increased their beliefs with respect either to a single hypothesis or to both hypotheses. We fitted mixed-effects models and we used the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) values to compare the competing models of the value of the obtained evidence. Overall, the experiments showed that measure Z was the best-fitting model of participants' judgments of the value of obtained answers. We discussed the implications for the human hypothesis-evaluation process.

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“…27 People often fail to understand that probabilities of events in a set that includes all possibilities (eg, percentage chance of polyp presence plus percentage chance of polyp absence) must add up to 100%, 28 that the probabilities of independent events must be multiplied and not added, and that the conditional probability of Event A given Event B does not necessarily equal the probability of Event B given Event A. 29 For example, the probability of getting breast cancer given that one has a mutated BRCA1 or BRCA2 gene is 60% to 80%, 30 but the probability that a woman who develops breast cancer also happens to have a BRCA mutation is substantially lower. Similarly, the percentage of smokers who get lung cancer is substantially lower than the percentage of people having lung cancer who smoke.…”

Section: Percentage Scalesmentioning

confidence: 99%

Cancer Risk Elicitation and Communication: Lessons from the Psychology of Risk Perception

Klein

Stefanek

2007

CA: A Cancer Journal for Clinicians

143

129

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Cancer risk perceptions are a key predictor of risk-reduction practices, health behaviors, and processing of cancer information. Nevertheless, patients and the general public (as well as health care providers) exhibit a number of errors and biases in the way they think about risk, such that their risk perceptions and decisions deviate greatly from those prescribed by normative decision models and by experts in risk assessment. For example, people are more likely to engage in screening behaviors such as mammography when faced with loss-based messages than gain-framed messages, and they often ignore the base rate of a given disease when assessing their own risk of obtaining this disease. In this article, we review many of the psychological processes that underlie risk perception and discuss how these processes lead to such deviations. Among these processes are difficulties with use of numerical information (innumeracy), cognitive processes (eg, use of time-saving heuristics), motivational factors (eg, loss and regret aversion), and emotion. We conclude with suggestions for future research in the area, as well as implications for improving the elicitation and communication of personal cancer risk.

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The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

Cited by 111 publications

References 35 publications

Is the mind Bayesian? The case for agnosticism

Is the mind Bayesian? The case for agnosticism

Evidence evaluation: Measure Z corresponds to human utility judgments better than measure L and optimal-experimental-design models.

Cancer Risk Elicitation and Communication: Lessons from the Psychology of Risk Perception

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