The Probability of Conditionals

Girotto, Vittorio; Johnson‐Laird, P. N.

doi:10.2117/psysoc.2004.207

Cited by 41 publications

(46 citation statements)

References 23 publications

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“…It can also be noted that the model p q is not part of the initial representation because all the disjunctions are not true in this case. cases and p cases or the conjunctive probability if they consider simply the proportion of cases in which the conditional is true among all the possible cases (Evans et al, 2003;Girotto & Johnson-Laird, 2004). This explains also why, as Evans et al (2005) noted, the probability of a conditional is never judged to be equal to not p or q.…”

Section: A Theoretical Proposalmentioning

confidence: 99%

Mental models and the suppositional account of conditionals.

Barrouillet

Gauffroy

Lecas

2008

Psychological Review

122

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The mental model theory of conditional reasoning presented by P. N. Johnson-Laird and R. M. J. Byrne (2002) has recently been the subject of criticisms (e.g., J. St. B. T. Evans, D. E. Over, & S. J. Handley, 2005). The authors argue that the theoretical conflict can be resolved by differentiating 2 kinds of reasoning, reasoning about possibilities given the truth of assertions and reasoning about the truth of assertions given possibilities. The standard mental model theory accounts for the former kind of reasoning but does not adequately account for the latter, contrary to the suppositional approach favored by J. St. B. T. Evans et al. (2005). The authors thus propose a modified mental model theory of conditionals that reconciles the 2 theoretical approaches. It is demonstrated that this theory is able to explain the key findings that have been opposed to the standard theory by J. St. B. T. Evans et al. and makes new predictions that are empirically verified.

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Section: A Theoretical Proposalmentioning

confidence: 99%

Mental models and the suppositional account of conditionals.

Barrouillet

Gauffroy

Lecas

2008

Psychological Review

122

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“…The second task that is claimed to distinguish the suppositional theory from the mental models account is the probability-of-conditionals tasks (Evans et al, 2003;Evans, Ellis, & Newstead, 1996;Girotto & Johnson-Laird, 2004;Hadjichristidis et al, 2001;Oberauer & Wilhelm, 2003). In a typical task, participants are given information about the relative frequency of TT, TF, FT, and FF cases and are asked to judge the probability that the conditional statement is true.…”

Section: B4 (Tt) B7 (Tf) G4 (Ft) L8 (Ff)mentioning

confidence: 99%

“…The frequency distributions presented allow computation of several different probabilities that could form the basis for the judged probability of the conditional statements. On such tasks, choices are generally inconsistent with the probability of the material conditional-P(not-p or q)-although Girotto and Johnson-Laird (2004) reported some cases. The most common response is that predicted by the suppositional theory, to give the conditional probability P(q|p).…”

Section: B4 (Tt) B7 (Tf) G4 (Ft) L8 (Ff)mentioning

confidence: 99%

Thinking about conditionals: A study of individual differences

et al. 2007

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Recent studies have shown the existence of two qualitatively distinct groups of people based on how they judge the probability of a conditional statement. The present study was designed to test whether these differences are rooted in distinctive means of processing conditional statements and whether they are linked to differences in general intelligence. In the study, each of 120 participants completed three separate cognitive tasks involving the processing of abstract conditional statements-the probability-of-conditionals task, the conditional truth table task, and the conditional inference task-in addition to completing a test of general intelligence (AH4). The results showed a number of predicted effects: People responding with conditional (rather than conjunctive) probabilities on the first task were higher in cognitive ability, showed reasoning patterns more consistent with a suppositional treatment of the conditional, and showed a strongly "defective" truth table pattern. The results include several novel findings and post challenges to contemporary psychological theories of conditionals.

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“…A major mystery about such estimates is the mental operations that underlie them, and an even bigger mystery is where the numbers come from and what determines their magnitudes. To solve these mysteries, we developed a theory based on mental models [10,11] and, unlike previous accounts of the psychology of probabilities, we have implemented the theory in a computer program that yields estimates of the probabilities of unique events. The theory and its computer implementation predict the occurrence of violations of the probability calculus both in numerical and in verbal estimates of probabilities.…”

Section: Introductionmentioning

confidence: 99%

The Probabilities of Unique Events

Khemlani¹,

Lotstein²,

Johnson‐Laird³

2012

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Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an intuitive non-numerical system capable only of simple procedures, and a deliberative system that maps intuitions into numbers. The theory predicts that estimates of the probabilities of conjunctions should often tend to split the difference between the probabilities of the two conjuncts. We report two experiments showing that individuals commit such violations of the probability calculus, and corroborating other predictions of the theory, e.g., individuals err in the same way even when they make non-numerical verbal estimates, such as that an event is highly improbable.

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The Probability of Conditionals

Cited by 41 publications

References 23 publications

Mental models and the suppositional account of conditionals.

Mental models and the suppositional account of conditionals.

Thinking about conditionals: A study of individual differences

The Probabilities of Unique Events

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