The Conjunction Effect
The conjunction effect occurs when a combination of events is judged more probable than a broader event that contains it. A plausible added cause can make a narrower scenario feel more likely. Support theory relates this to how descriptions make supporting possibilities accessible.
THE IDEA
The Conjunction Effect
Considerable research has documented the conjunction effect, in which a conjunction AB is judged more probable than one of its constituents A. The effect is strongest when an event that initially seems unlikely (e.g., a massive flood in North America in which more than 1,000 people drown) is supplemented by a plausible cause or qualification (e.g., an earthquake in California causing a flood in which more than 1,000 people drown), yielding a conjunction that is perceived as more probable than the initially implausible event of which it is a proper subset (Tversky & Kahneman, 1983). Support theory suggests that the implicit hypothesis A is not unpacked into the coextensional disjunction AB ∨ A
which partitions A into cases with B and cases without B. The conjunction is one component of that partition. As a result, evidence supporting AB is not taken to support A. In the flood problem, for instance, the possibility of a flood caused by an earthquake may not come readily to mind; thus, unless it is mentioned explicitly, it does not contribute any support to the (implicit) flood hypothesis. Support theory implies that the conjunction effect would be eliminated in these problems if the implicit disjunction were unpacked before its evaluation (e.g., if subjects were reminded that a flood might be caused by excessive rainfall or by structural damage to a reservoir caused by an earthquake, an engineering error, sabotage, etc.).
The greater tendency to unpack either the focal or the residual hypothesis in a frequentistic formulation may help explain the finding that conjunction effects are attenuated, although not eliminated, when subjects estimate frequency rather than probability. For example, the proportion of subjects who judged the conjunction “X is over 55 years old and has had at least one heart attack” as more probable than the constituent event “X has had at least one heart attack” was significantly greater in a probabilistic formulation than in a frequentistic formulation (Tversky & Kahneman, 1983).
It might be instructive to distinguish two different unpacking operations. In conjunctive unpacking, an (implicit) hypothesis (e.g., nurse) is broken down into exclusive conjunctions (e.g., male nurse and female nurse). Most, but not all initial demonstrations of the conjunction effect were based on conjunctive unpacking. In categorical unpacking, a superordinate category (e.g., unnatural death) is broken down into its “natural” components (e.g., car accident, drowning, homicide). Most of the demonstrations reported in this chapter are based on categorical unpacking. A conjunction effect using categorical unpacking has been described by Bar-Hillel and Neter (1993; Chapter 3, this volume).
When to use it
Risk assessment: When evaluating the likelihood of complex events, be aware that adding plausible details can inflate perceived probability.
Medical reasoning: Compare the joint event of a disease and a symptom with the disease event in the same population. Keep this separate from the probability of disease given an observed symptom.
Legal reasoning: Check whether a detailed account is being judged more likely than a broader event that includes it.
Business forecasting: Disaggregate compound scenarios to avoid overestimating the probability of specific combinations of events.
FROM THEORY TO EVERYDAY LIFE
In practice
Massive flood and earthquake
A massive flood in North America causing more than 1,000 deaths is judged less probable than an earthquake in California causing a flood causing more than 1,000 deaths, even though the latter is a subset of the former.
Heart attack and age
The conjunction 'X is over 55 years old and has had at least one heart attack' is judged more probable than the single event 'X has had at least one heart attack' in probabilistic formulation, but the effect is attenuated in frequentistic formulation.
A MOMENT TO REFLECT
Put it to work.
Think of a time when you judged a specific scenario as more likely than a general one. How did the addition of details influence your probability estimate?
How might unpacking the possible causes of an event (e.g., a flood could be from rain, earthquake, engineering failure) affect your judgment of its probability?
In what real-life situations might the conjunction effect lead to overestimation of risk, and how can you guard against it?
References
- Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment — Tversky, A., & Kahneman, D. (1983)
- How alike is it versus how likely is it: A disjunction fallacy in probability judgments — Bar-Hillel, M., & Neter, E. (1993)
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)