The conjunction rule states that the probability of both A and B happening cannot exceed the probability of either A or B happening. The probability that I will roll a 6 on a die and flip heads on a coin, for example, cannot be greater than the probability that I will roll 6 on a die or flip heads. The conjunction fallacy occurs when this rule is violated.
Psychologists and Nobel prize winners Tversky and Kahneman demonstrated this with the case of Linda. Linda was described as “31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations”. Participants, having read this description, were asked to rank the probability of various statements about Linda being true. These included:
(1) Linda is a bank teller
(2) Linda is a bank teller and active in the feminist movement
A large majority of respondents thought (2) was more likely than (1). This violates the conjunction rule, as the probability of Linda being both a bank teller and active in the feminist movement, cannot be greater than the probability of her being only one of these (a bank teller). The problem is that statement (2) seems more representative of Linda as described in the passage, and it mistakenly deemed to be more likely.
The conjunction fallacy has important consequences for the legal system, as it often appears in the construction of plausible causal scenarios. Tversky and Kahneman also studied responses to John P, described as a defendant with prior convictions for smuggling precious stones and metals. Respondents were asked to consider the likelihood that:
(1) John is a drug addict
(2) John killed one of his employees
Only 23% of respondents thought it was more likely that John was a murderer than an addict. However, when option (2) was changed to “killed one of his employees to prevent them from talking to the police”, around half of respondents thought he was more likely to be a murderer than an addict.
The rules of probability tell us is that the more general a statement is, the more probable it is, and that every detail added to a series of events makes that series less likely. Just as it is more likely that I will see a car outside my window tomorrow than a red car, and more likely that I see a red car tomorrow than a red car with a dog in the back seat, it is more likely that John is a murderer that that he murdered specifically to prevent an employee talking to the police.
The problem is that extra detail gives rise to a more fathomable scenario; condemning John without any evident motive may seem premature, and the additional information makes the proposition seem more salient, more comprehensible, and (mistakenly) more probable.
This mistake can be costly to defendants who are faced with eloquent, detailed, but unproven hypotheses about why and how they have broken the law. As lawyers, then, we must be careful to distinguish between causal scenarios that are supported by evidence, and speculative storytelling. In the latter, every speculative detail doesn’t just cloud judgement and complicate decision-making, it dramatically reduces the likelihood of the explanation being true at all.
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological review, 90(4), 293.
Tversky, A., & Kahneman, D. (1981). Judgments of and by Representativeness (No. TR-3). Stanford University Department of Psychology