Subadditivity in Probability Judgments
Subadditivity occurs when the sum of probabilities assigned to specific, unpacked outcomes exceeds the probability of the more general, packed outcome, violating probability theory. This cognitive bias is demonstrated in experiments where subjects overestimate percentages of specific categories (e.g., number of children) compared to broader groupings.
THE IDEA
The text describes two experiments on subadditivity and suggestibility. In Study 2, Stanford undergraduates estimated the percentage of U.S. married couples with a given number of children (0–9), using the last digit of their phone numbers to assign the category. The sum of the mean estimates across categories was 1.99 (far above 1), showing strong subadditivity even when the hypothesis selection was non-informative. Overestimation occurred for all categories except childless couples, and the excess was not due to small probability overestimation alone. In a follow-up, subjects estimated percentages for complementary pairs (e.g., "less than 3" vs. "3 or more"), and estimates were roughly additive (97.5% and 96.3%), consistent with support theory and ruling out focal hypothesis bias.
When to use it
Evaluating risk in insurance underwriting where specific causes of loss are unpacked from a general category.
Forecasting project risks by breaking down overall uncertainty into specific failure modes.
Improving survey design to avoid inflated probability estimates when asking about detailed subcategories.
Teaching why statistical categories should be exhaustive and mutually exclusive.
FROM THEORY TO EVERYDAY LIFE
In practice
Experiment 1: Estimating Number of Children
Stanford undergraduates (N=196) estimated the percentage of U.S. married couples with exactly 0–9 children, using the last digit of their phone numbers to select the focal category. The sum of mean estimates across all categories was 1.99 (median sum 1.80), indicating subadditivity. Overestimation was greatest for couples with 2 children, and the sum for 0–3 children (each exceeding 25%) was 1.45, ruling out small-probability overestimation as the sole cause.
Experiment 2: Complementary Hypotheses
Another group (N=139) estimated percentages for complementary pairs: "less than 3" vs. "3 or more" and "less than 5" vs. "5 or more." The estimates for each pair summed to 97.5% and 96.3%, respectively, showing near-additivity and supporting the idea that subadditivity is specific to unpacked, non-complementary hypotheses.
A MOMENT TO REFLECT
Put it to work.
Why does unpacking a broad category into specific subcategories often lead to probability estimates that sum to more than the original category's probability?
How might subadditivity affect real-world risk assessments, such as estimating the likelihood of different causes of death?
Can you think of a situation where ignoring subadditivity could lead to flawed decisions or overconfident predictions?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)