1. The probability of conditionals: A review
- Author
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Marco Ragni, Philip N. Johnson-Laird, and Miguel López-Astorga
- Subjects
Model theory ,Logic ,Experimental and Cognitive Psychology ,Models, Psychological ,050105 experimental psychology ,Theoretical/Review ,Mental models ,Judgment ,03 medical and health sciences ,0302 clinical medicine ,Arts and Humanities (miscellaneous) ,Joint probability distribution ,Subadditivity ,Developmental and Educational Psychology ,Humans ,0501 psychology and cognitive sciences ,Problem Solving ,Axiom ,Conditional probabilities ,Probability ,Corresponding conditional ,Discrete mathematics ,Probabilities ,SARS-CoV-2 ,05 social sciences ,Probabilistic logic ,COVID-19 ,Conditional probability ,Term (logic) ,The Equation ,Conditionals ,Psychology ,030217 neurology & neurosurgery - Abstract
A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory. Supplementary Information The online version contains supplementary material available at 10.3758/s13423-021-01938-5.
- Published
- 2021