Subadditivity Effect
Subadditivity is the cognitive bias where the sum of judged probabilities of mutually exclusive events exceeds 1, often amplified when additional evidence supports multiple hypotheses simultaneously.
THE IDEA
Subadditivity in Probability Judgment
This bias refers to the tendency for people to assign probabilities to mutually exclusive events that sum to more than 1, violating normative probability theory. Subadditivity is particularly enhanced when new information increases the apparent plausibility of multiple hypotheses simultaneously.
Key Findings from Evidence
Crime Suspects Study (Study 4):
- Participants rated suspiciousness and probability of guilt for each suspect in two crime cases (low- and high-information conditions).
- In all conditions, sums of probability judgments and suspiciousness ratings exceeded 1. The probability totals support the subadditivity claim; suspiciousness ratings need not obey the same normalization rule.
- With added information, suspiciousness increased for all but one suspect (the artist in the murder case, who received an alibi), leading to enhanced subadditivity.
- Statistical tests showed significantly greater ratings under high-information than low-information (p < .001).
Normative Contrast: For mutually exclusive and exhaustive alternatives, the total probability must remain fixed. Increasing some probabilities therefore requires decreases elsewhere. The reported judgments did not consistently respect that constraint.
Previous Research:
- Robinson and Hastie (1985) and Van Wallendael & Hastie (1990) found similar subadditivity using within-subject assessments, with unpacking factors around 2.
- These authors rejected the Bayesian model and proposed Shafer's theory, but the observed subadditivity is inconsistent with both.
Baseball Wins Study (Peterson & Pitz, 1988):
- Participants estimated probabilities for intervals of wins (e.g., <80, 80-88, >88) based on 1, 2, or 3 cues.
- As cues increased, probabilities for all intervals rose, showing enhanced subadditivity.
- Unpacking factors: 1.26 (1 cue), 1.61 (2 cues), 3.86 (3 cues).
- This effect occurred even when evidence favored some hypotheses more than others, demonstrating robustness.
When to use it
Legal reasoning: Lawyers might overestimate the probability of each suspect's guilt when presented with cumulative evidence.
Project management: forecasts for mutually exclusive outcomes may sum to more than 100%. Risks that can occur together need not satisfy that constraint.
Diagnostic reasoning: probabilities assigned to mutually exclusive explanations should not total more than 1. Conditions that can coexist require a different comparison.
Forecasting: Analysts could overestimate the likelihood of several mutually exclusive events (e.g., economic scenarios) when faced with mixed data.
FROM THEORY TO EVERYDAY LIFE
In practice
Crime Suspects: Murder Case
In a hypothetical murder case with multiple suspects (artist, etc.), participants rated suspicion and probability of guilt. Adding evidence (e.g., alibi for the artist) increased suspicion for all other suspects, but also increased probability for all suspects except the artist, leading to summed probabilities > 1.
Baseball Season Wins
Participants estimated probabilities for three intervals of wins (<80, 80-88, >88) based on cues like batting average. As more cues were provided, probabilities for all intervals increased, summing to more than 1, with unpacking factors up to 3.86.
A MOMENT TO REFLECT
Put it to work.
Think of a time when you estimated the likelihood of several competing outcomes and their total exceeded 100%. What factors might have caused this?
How could the subadditivity effect distort risk assessments in fields like law or medicine?
If you were designing a decision support system, how would you help users avoid summing probability judgments beyond 1?
Often confused with
References
- Robinson & Hastie (1985) — Robinson, L. B., & Hastie, R. (1985)
- Van Wallendael & Hastie (1990) — Van Wallendael, L. R., & Hastie, R. (1990)
- Peterson & Pitz (1988) — Peterson, D. K., & Pitz, G. F. (1988)
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)