The probability of conditionals: A review

Area of Science:

• Cognitive Science
• Probability Theory
• Psychology

Background:

• The probability of a conditional statement is often equated with conditional probability: p(if A then C) = p(C|A).
• This 'Equation' is frequently treated as axiomatic in probabilistic theories.
• The theory of mental models posits that this Equation derives from the meaning of conditionals.

Purpose of the Study:

• To investigate how intuitive (System 1) and deliberative (System 2) reasoning processes affect the estimation of conditional probabilities.
• To examine whether intuitive mental models lead to errors in estimating conditional probabilities, particularly for unique events.
• To provide empirical support for the theory of mental models in explaining probability estimation biases.

Main Methods:

• Participants estimated the probability of conditional statements and their constituent clauses.
• The study focused on unique events, such as 'If covid-19 disappears in the USA, then Biden will run for a second term'.
• Analysis of joint probability distributions derived from intuitive estimates was conducted.

Main Results:

• Intuitive mental models (System 1) do not represent false possibilities, leading to errors where p(if A then C) is estimated as p(A & C).
• Estimates for conditionals about unique events and their clauses resulted in joint probability distributions exceeding 100%.
• This error is inconsistent with the probability calculus and demonstrates a massive bias in intuitive probability estimation.

Conclusions:

• Deliberative reasoning (System 2) correctly yields conditional probabilities consistent with the Equation.
• Intuitive reasoning (System 1) produces systematic errors in estimating conditional probabilities, particularly for unique events.
• The findings corroborate the theory of mental models by demonstrating how different reasoning systems lead to distinct probabilistic judgments.