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conjunction_fallacy
The conjunction fallacy occurs when people judge the probability of two events occurring together (a conjunction) as more likely than the probability of either event occurring alone. This violates a basic axiom of probability theory: P(A and B) can never exceed P(A) or P(B). The fallacy is driven by representativeness: when the conjunction creates a more coherent, plausible-sounding narrative, it feels more probable.
Linda is 31, outspoken, and majored in philosophy. She was active in anti-nuclear demonstrations. People rate 'Linda is a bank teller and active in the feminist movement' as MORE probable than 'Linda is a bank teller,' even though the conjunction must be less probable by the laws of probability.
Voters are told that a candidate is a former military officer who speaks frequently about national security. When asked to rank likelihoods, most say it is more probable that 'he will cut social programs AND increase defense spending' than simply 'he will increase defense spending,' even though the conjunction cannot exceed the probability of either component alone.
A news headline describes a tech entrepreneur as young, rebellious, and college-dropout. Readers rate 'She founded a startup AND dropped out to pursue it' as more likely than simply 'She dropped out of college,' because the added detail feels narratively coherent despite making the scenario statistically less probable.
Binary (yes/no) questions an LLM must answer to identify this aspect:
Is the probability of a specific, detailed scenario being rated as higher than a more general one?
Type: binaryDoes the more detailed scenario add conditions that should reduce probability?
Type: binaryIs the representativeness or narrative plausibility of a scenario being confused with its probability?
Type: binaryDoes the probability assessment violate the conjunction rule?
Type: binaryThe conjunction fallacy occurs when people judge the probability of two events occurring together (a conjunction) as more likely than the probability of either event occurring alone. This violates a basic axiom of probability theory: P(A and B) can never exceed P(A) or P(B). The fallacy is driven by representativeness: when the conjunction creates a more coherent, plausible-sounding narrative, it feels more probable.
Adding detail that matches a stereotype makes a description more representative and coherent. The brain uses narrative plausibility as a proxy for probability, and a specific vivid scenario feels more 'real' than a vague general one.
Apply the subset rule: 'feminist bank tellers' is a subset of 'bank tellers,' so the subset can never be more probable. Use Venn diagrams to visualize that the conjunction is always contained within each individual category.
The conjunction fallacy affects jury reasoning (detailed alibis sound more credible), risk assessment (specific threat scenarios rated as more likely than general ones), and intelligence analysis.
Use these tools to detect, analyze, or train this aspect.