Disjunction Rule Violation
The disjunction rule states that the probability of a disjunctive event (A or B) cannot be less than the probability of any individual disjunct. Studies show that people often violate this rule when ranking outcomes by willingness to bet or by perceived probability.
THE IDEA
Results and Discussion
Table 3.2, which contains the reported results, is not included. The top row shows the rates of violation of the disjunction rule for the “rank the outcomes by your willingness-to-bet on them” formulation, the middle row shows the rates for the “rank the outcomes by their probability” formulation, and the bottom row combines the two conditions. Comparing willingness to bet with judged probability assumes comparable payoffs and betting terms.
Judging an event by how representative or easy to recall it seems can conflict with the logical relation between a component and a broader event. For example, the probability of a specific outcome (e.g., a heart attack) may be judged higher than the probability of a more general category (e.g., a heart attack or stroke), violating the disjunction rule.
When to use it
Risk assessment in finance: check that the probability of either stock A or stock B losing value is at least as high as the probability of either individual stock losing. A portfolio’s overall return is a different event.
Medical diagnosis: avoiding the error of estimating a lower probability for a symptom being due to one of several diseases than for a single specific disease.
Legal reasoning: evaluating the likelihood that a defendant is guilty of at least one of several charges, which must be at least as high as for any single charge.
Everyday prediction: when forecasting events, checking that the probability of a disjunction is not inadvertently set too low.
FROM THEORY TO EVERYDAY LIFE
In practice
Medical Diagnosis
A doctor might estimate the chance that a patient has lung cancer as 20% but estimate the chance of either lung cancer or bronchitis as only 15%, violating the disjunction rule because the disjunction must be at least as likely as the component.
Betting Scenario
As an illustration, a bettor ranks an athlete winning a race as more likely than that athlete either winning or placing. Because the broader event includes winning, it cannot have a lower probability. A comparison based on willingness to bet would also need to account for the betting terms.
A MOMENT TO REFLECT
Put it to work.
Can you recall a time when you assigned a lower probability to a broader category than to one of its specific instances? How might the disjunction rule have helped?
When evaluating risks, why is it important to remember that the probability of 'A or B' must be at least as large as the probability of A alone?
How could the disjunction rule be taught to improve reasoning in medical or financial decision-making?
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)