The probability of conditionals: A review

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.

A Quantitative Symbolic Approach to Individual Human Reasoning

“…Interestingly, whenever a suppression effect occurs in a group, ASP also generates more models compared to the other groups. This seems to agree with the assumption that inferences which leads to multiple models should be more difficult than the ones on a single model (López-Astorga et al, 2021).…”

“…PHM does not suggest how probabilities are computed, i.e. no implemented algorithm exists (López-Astorga, Ragni, & Johnson-Laird, 2021). The (Mental) Model Theory (Johnson-Laird, 1983) assumes that humans reason by constructing and manipulating mental models, which illustrate the possibilities of how the world is perceived by the reasoner (Khemlani & Johnson-Laird, 2013).…”

“…The model theory with naive probabilities (Johnson-Laird, Legrenzi, Girotto, Legrenzi, & Caverni, 1999) provides a simple algorithm without using Bayes's theorem, for computing subjective probabilities and was further extended (Khemlani, Lotstein, & Johnson-Laird, 2015;Khemlani & Johnson-Laird, 2016). These two theories seem to have conflicting viewpoints (Oaksford & Chater, 2020;Knauff & Gazzo Castañeda, 2021;Oaksford, 2021;Over, 2021) and so far, there is no agreement on whether an integration is possible (López-Astorga et al, 2021;Over, 2021).…”

In Favor of Logical Form

“…However, regarding this, two points can be made. First, the mental model theorists have tried to respond to most of these criticisms (e.g, Johnson-Laird, Khemlani, & Goodwin, 2015b;Johnson-Laird & Ragni, 2019;López-Astorga, Ragni, & Johnson-Laird, 2021). Second, in many cases, as shown below, those criticisms do not have an influence on the arguments of the present paper.…”

A Conceptual Framework for Constructing Decision Policies by Processing the Possibilities in Mental Models of Dynamic Systems with the Cognitive Theory of Mental Models

“…Two decades ago, the formal rules approach seemed to be a strong competitor for the model theory (Doyle and Ford, 1998), but recent comparative research suggests that the model theory overcomes several paradoxes which the remaining two types of theories leave unanswered (López-Astorga, Ragni, and Johnson-Laird, 2022;Ragni and Johnson-Laird, 2020b;Ragni, Kola, and Johnson-Laird, 2018). Since both research streams work on mental models, we argue for a fruitful combined use.…”