Recipe · serves one confident error
Subadditivity Effect
The judged probability of an implicit (packed) hypothesis is systematically lower than the sum of judged probabilities assigned to its explicitly unpacked components, violating the additivity axiom of probability theory.
Difficulty to avoid: strong grounding
Kitchen-testedIngredients · what the mind brings
Method · how they combine
Support theory (Tversky & Koehler, 1994) proposes that subjective probability reflects the balance of evidential support between a focal hypothesis and its alternatives.
uses Support Theory
When a hypothesis is packed (implicit), people generate less support for it because the component possibilities are not explicitly mentioned.
uses Conjunction Fallacy
Unpacking makes each component salient, generating additional support that sums to more than the packed judgment.
uses Availability Heuristic
Working memory capacity and cognitive load moderate the effect: Dougherty & Hunter (2003) found subadditivity increases under time constraints and decreases with higher working memory span.
uses Support Theory
Note · Alternative explanations include stochastic error models (Erev, Wallsten, & Budescu, 1994) where regression toward the midpoint produces subadditivity, and an 'ignorance prior' account where judgments bias toward 1/n for each event. Bearden & Wallsten (in press) showed subadditivity appears more pronounced when using means versus medians. The balance of evidence currently favors a hybrid of support theory and stochastic processes.
Tested variations
Classic causes-of-death unpacking. When participants judged P(death from cancer)=18%, P(heart attack)=22%, and P(other natural causes)=33%, the sum was 73%. But a separate group judged P(death from natural cause)=58%. The 15-percentage-point gap demonstrates subadditivity.
Tversky & Koehler, 1994 · Multiple samples of university students across several experiments
Physicians' diagnostic probability judgments. Physicians' summed probability estimates averaged 164% when unpacked, demonstrating substantial subadditivity. They systematically discounted unspecified alternatives, consistent with support theory predictions.
Redelmeier, Koehler, Liberman, & Tversky, 1995 · n = 59 physicians (residents and attending physicians)
Search and rescue probability planning. 78% of planners demonstrated subadditivity. Unpacking the residual hypothesis increased estimated probability that the subject had left the search area by over 4 percentage points compared to those who unpacked the focal hypothesis.
Koester, Gerecke, & Welch, 2017 · n = 32 experienced male search-and-rescue planners
Tested rating — replication
The subadditivity effect has been replicated across diverse populations including physicians (Redelmeier et al., 1995), options traders (Fox et al., 1996), lawyers (Fox & Birke, 2002), and search-and-rescue planners (Koester et al., 2017). The effect has also been found with probability judgments for sports outcomes, causes of death, and medical diagnoses. However, the mechanism remains debated between support theory and stochastic error interpretations.
Substitution that changes the dish
Require that all probability estimates sum to exactly 100% before finalizing judgments; assess the whole distribution of hypotheses together rather than individually. Witteman et al. (2007) found enforcing the additivity constraint reduces subadditivity.
Research on probability assessment scales shows that forcing estimates to sum to 100% and using numerical rather than verbal scales reduces subadditivity. Evaluating the entire distribution simultaneously rather than component-by-component also helps.
Reader submissions · seen in the wild
Physicians' diagnostic probability estimates summing to 164% · 1995
Redelmeier et al. (1995) found that when physicians unpacked diagnostic or prognostic hypotheses for clinical vignettes, their summed probability estimates averaged 164%. This dramatic violation of probability additivity suggests physicians systematically discount unspecified alternatives.
Search-and-rescue planning with unpacking · 2017
Koester et al. (2017) found that 78% of experienced search-and-rescue planners showed subadditivity when assigning probabilities to search areas. Unpacking the residual hypothesis (subject outside search area) increased probability estimates by over 4 percentage points, potentially delaying search expansion.
Probability scale comparison in medical diagnosis · 2007
Witteman et al. (2007) found subadditivity in physicians using all three probability assessment scales (verbal, numerical, double). Verbal scales produced significantly more subadditivity upon unpacking than numerical scales in one vignette.
Tasting note
When probability estimates for a set of possible outcomes sum to more than 100%; when breaking down a broad category into subcategories inflates the perceived total likelihood; when physicians assign diagnostic probabilities that exceed unity when combined.