Disjunction Fallacy (Disjunction Effect)
The disjunction fallacy occurs when a broader, inclusive event is judged less probable than an event it contains—for example, humanities less probable than literature. Conversational preferences for specific statements are one proposed explanation for this probability error.
THE IDEA
Here, the disjunction fallacy refers to judging the probability of a disjunction (an 'or' statement or inclusive category) to be lower than the probability of one of its constituents. This contradicts the normative principle of probability: P(A or B) ≥ P(A) and P(A or B) ≥ P(B).
Background and Experiment
Tversky and Kahneman (1983) and subsequent research (e.g., Morier & Borgida, 1984) explored this phenomenon. In one paradigm, participants were given descriptions of individuals (e.g., 'Danielle') and asked to rank the probability that the described person belonged to various categories, which included pairs of a basic level category (e.g., 'literature') and its superordinate (e.g., 'humanities'). For example, if Danielle is described as a literature major, participants might rate 'humanities' as less probable than 'literature', even though literature is a subset of humanities.
Linguistic and Pragmatic Factors
Two interpretive concerns matter:
- Interpretation of disjunctions: Participants might interpret a disjunctive category (e.g., 'one of the European countries') in a subtractive sense (excluding Switzerland). To counter this, instructions explicitly warned against such exclusion.
- Conversational implicature: According to Gricean maxims, a cooperative speaker would not assert a broader category (e.g., 'humanities') if they could assert a more specific one (e.g., 'literature'). Thus, asserting 'humanities' implies uncertainty about the specific category. However, in logical terms, 'humanities' is still true if 'literature' is true.
Betting Paradigm
To disentangle assertion from probability judgment, a betting paradigm was used where participants ranked categories by their willingness to bet on membership. In betting, logical entailment overrides conversational implicature: a bet on 'humanities' is always at least as likely to win as a bet on 'literature', because any case that satisfies 'literature' also satisfies 'humanities'. The results showed that participants' probability rankings followed conversational norms (favoring specificity), while betting rankings were more logical.
Implications
The disjunction fallacy highlights the conflict between pragmatic communication and logical reasoning. It is related to the conjunction fallacy (where a conjunction is judged more probable than a constituent) but is distinct in its focus on disjunctions. When comparing probabilities, check whether one event includes another before relying on how informative each description sounds.
When to use it
When comparing a specific claim with a broader one, distinguish the probability that it is true from its informativeness or its adequacy for a particular purpose.
In risk assessment, when evaluating the probability of an event, remember that disjunctive events are at least as likely as their components; e.g., 'a natural disaster or terrorist attack' is at least as likely as 'a terrorist attack' alone.
In medical diagnosis, a patient's symptoms might fit a broad category (e.g., 'autoimmune disease') more than a specific one (e.g., 'lupus'), but the broad diagnosis should not be discounted.
In product testing, the probability of a defect under any of several conditions is at least as high as the probability under one of those conditions. Check the full set of relevant cases.
FROM THEORY TO EVERYDAY LIFE
In practice
Danielle's Field of Study
Participants read a description of a student named Danielle and were asked to rank the probability that she majored in various fields. The list included 'literature' (basic level) and 'humanities' (superordinate). Despite literature being a subset of humanities, participants often ranked 'humanities' as less probable than 'literature', illustrating the disjunction fallacy.
Betting on Membership
In a betting variant, participants compare bets on (A) Danielle being a literature major and (B) Danielle being a humanities major. With the same stakes and payoff, the broader bet cannot lose in a case where the narrower one wins. This format separates a bet’s winning conditions from the conversational appeal of a specific description.
A MOMENT TO REFLECT
Put it to work.
Recall a time when you assumed a broader category was less likely than a specific instance. How did that affect your decision?
Why might a cooperative speaker avoid stating a broader category when a specific one is known? How does this relate to the disjunction fallacy?
How could understanding the disjunction fallacy help improve your reasoning in legal or medical contexts where probabilities are involved?
Often confused with
References
- Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment — Tversky, A., & Kahneman, D. (1983)
- A replication and extension of the conjunction fallacy — Morier, D., & Borgida, E. (1984)
- Tests of the generality of the conjunction fallacy — Wolford, G., Taylor, H. A., & Beck, J. R. (1990)
- The Logic of Conditionals — Adams, E. W. (1975)
CONTINUE THE CONVERSATION
Source texts
- Heuristics and Biases The Psychology of Intuitive Judgment (Thomas Gilovich, Dale Griffin, Daniel Kahneman)