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

Abstract

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). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62], and we observe lower performance levels than those in the original article.

Keywords:

• Probability
• Mental models
• Elicitation of estimates
• Extensional reasoning

ORCID

Thierry Chevalley http://orcid.org/0000-0002-3371-8073

Walter Schaeken http://orcid.org/0000-0002-5220-1643

Notes

¹The four items included in the index are p(A), p(A and B), p(A and ¬B ), and p(¬ A and ¬B ).

²In the analysis of variance (ANOVA), the type of premise factor has an F-value=76.32 with p < 2.2 × 10⁻¹⁶. We use factorial ANOVA for unordered predictors.

³A reviewer of the article by Johnson-Laird et al. (1999, p. 74) wrote “It is difficult for me to believe that a random sample of Chicagoans, for example, would have responded to such an ill-defined question with much more than a blank stare”.

⁴In the analysis of variance, the type of premise factor has an F-value = 4.741 with p < .01 for the logical norm and an F-value = 50.57 with p < 2.2 × 10⁻¹⁶ for the mental model theory forecast. We use factorial ANOVA to get the contribution to the explained variance of each effect.