Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62Crossref], PubMed], Web of Science ®] , Google Scholar]], and we observe lower performance levels than those in the original article.