Naive probability: a mental model theory of extensional reasoning

Area of Science:

• Cognitive Psychology
• Decision Science
• Probability Theory

Background:

• Individuals often reason about probabilities without formal training in probability calculus.
• Existing models of probabilistic reasoning may not fully capture intuitive or 'naive' probability judgments.
• Understanding naive probability is crucial for explaining cognitive biases and illusions.

Purpose of the Study:

• To present a novel theory of naive probability that explains how individuals infer probabilities without formal calculus.
• To demonstrate how this theory accounts for both accurate probabilistic inferences and systematic biases.
• To provide a framework for understanding intuitive probability judgments and their underlying mechanisms.

Main Methods:

• The proposed theory models naive probability inference as an extensional process.
• Individuals construct mental models representing possible scenarios or outcomes.
• Probabilities are assigned based on the proportion of models supporting an event, with adjustments for prior beliefs.

Main Results:

• The theory successfully predicts reasoning phenomena related to absolute probabilities, including common biases.
• It accurately accounts for cognitive illusions observed in relative probability judgments.
• The model accommodates reasoning from numerical premises and explains inference of posterior probabilities without Bayes's theorem.

Conclusions:

• The theory offers a coherent explanation for naive probability judgments, integrating biases and accurate inferences.
• It challenges misconceptions about probabilistic reasoning and highlights the role of mental models.
• This framework advances our understanding of intuitive decision-making under uncertainty.