Subadditivity effect

The subadditivity effect is the tendency to judge probability of the whole to be less than the probabilities of the parts.

For instance, subjects in one experiment judged the probability of death from cancer in the United States was 18%, the probability from heart attack was 22%, and the probability of death from "other natural cause" was 33%. Other participants judged the probability of death from a natural cause was 58%. Natural causes are made up of precisely cancer, heart attack, and "other natural causes," however; the sum of the latter three probabilities was 73%, and not 58%. According to Tversky and Koehler (1994) this kind of result is observed consistently.

The same mechanisms may underlie an effect of familiarity on probability judgment. More familiar events are more available. This is known as the availability heuristic. We find it easier to think of reasons why these events will and will not happen. In an experiment carried out by Fox and Levav (2000), they asked students at Duke University which of two events was more likely to occur. The first one was "Duke men's basketball defeats UNC men’s basketball at Duke’s Cameron Indoor Stadium in January 1999," and the other one was "Duke men’s fencing defeats UNC men’s fencing at Duke’s Cameron Card Gym in January 1999." The researchers postulated that since Duke students are much more familiar with basketball than with fencing, 75% of the students thought the basketball victory was more likely. Other students answered the exact same questions, however, with Duke and UNC switched around. After the change, 44% of the students said that a UNC victory in basketball was more likely than a UNC victory in fencing. 44% plus 75% is 119%, which is larger than 100%, and only one such basketball game would be played. In this experiment, familiarity with basketball led subjects to think of the basketball event as more likely than the fencing event, regardless which basketball event was described.

References

* Baron, J. (in preparation). Thinking and deciding, 4th edition. New York: Cambridge University Press.
* Tversky, A., & Koehler, D. J. (1994). Support theory: A nonextentional representation of subjective probability. Psychological Review, 101, 547–567.
* Fox, C. R., & Levav, J. (2000). Familiarity bias and belief reversal in relative likelihood judgments. Organizational Behavior and Human Decision Processes, 82, 268–292.