Definition
The Fallacy of Conjunction (also known as the Conjunction Fallacy or the Linda Problem) is a formal logical fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. It violates the basic mathematical rule that the probability of two events occurring together () is always less than or equal to the probability of either one occurring alone ().
- How to read: “The probability of A intersect B is less than or equal to the probability of A.”
- Meaning: A conjunction adds requirements, shrinking the event space—“bank teller AND feminist” cannot be more likely than “bank teller.”
Why It Matters
This fallacy is why we find “conspiracy theories” more compelling than boring statistical probabilities. Our brains are narrative-seeking machines that prefer a “vivid story” over a “probable state.” Recognizing this bias is essential for risk management and forecasting; without it, we will consistently over-prepare for high-information, low-probability “scenarios” while being blindsided by simple, high-probability failures.
Core Concepts
- The Linda Problem: Respondents often judge it more likely that a person with certain characteristics (e.g., liberal, outspoken) is both a bank teller and a feminist, rather than just a bank teller.
- Narrative Vividness: We are deeply affected by vivid, available evidence. We prefer “believable” stories (conjunctions) over “probable” facts (single states).
- Brain Malfunction: If evidence is presented in a certain light (representativeness heuristic), the brain bypasses rational statistics and assigns higher probability to the more descriptive option.
- Self-Centered Logic: This fallacy is a root cause of assuming malice (intent + action) over simple error (action alone).