Naive Probability: A Mental Model Theory of Extensional Reasoning

• Published in: Psychological review 1999-01, Vol.106 (1), p.62-88
• Main Authors: Johnson-Laird, P. N, Legrenzi, Paolo, Girotto, Vittorio, Legrenzi, Maria Sonino, Caverni, Jean-Paul
• Format: Article
• Language: English
• Subjects: Bayes Theorem; Beliefs; Biological and medical sciences; Cognition; Cognition & reasoning; Cognition. Intelligence; Critical Thinking; Decision Making; Fundamental and applied biological sciences. Psychology; Human; Humans; Inductive Deductive Reasoning; Intuition; Logical Thinking; Mental Models; Models, Psychological; Probabilistic Reasoning; Probability; Probability Judgment; Probability Theory; Psychology; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Reasoning. Problem solving; Theories; Thinking Skills
• ISSN: 0033-295X; 1939-1471
• DOI: 10.1037/0033-295X.106.1.62

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning.