López-Astorga et al. review the probability of conditionals in PBR

Miguel López-Astorga, Marco Ragni, and Phil Johnson-Laird present a new review on the probability of conditionals in Psychonomic Bulletin & Review: their analysis focuses on the psychological plausibility of the proposal that the probability of expressions such as if A then C is equivalent to the conditional probability, p(C | A), i.e., the probability of C given that A is true. Here’s their 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.

and the article is available for download here.

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