Once information is gathered, can it be correctly interpreted? We obtain fragments of the truth, but can we be sure we understand its significance? Our initial reaction is to rely on “common sense.” But too often our first take on things can be inaccurate. We assume facts are supportive when in fact they may be neutral––or perhaps even adverse. During jury selection, for example, we draw inferences from brief verbal exchanges with others, hoping that the tip of iceberg will shed some light on what exists below the surface. In this regard, there’s a fallacy known as the “conjunction fallacy.”
“The conjunction fallacy (also known as the Linda problem) is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one. The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman. Although the description and person depicted are fictitious, Amos Tversky’s secretary at Stanford was named Linda Covington, and he named the famous character in the puzzle after her. Linda is 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. Which is more probable? Linda is a bank teller. Linda is a bank teller and is active in the feminist movement. The majority of those asked chose option 2. However, the probability of two events occurring together (in “conjunction“) is always less than or equal to the probability of either one occurring alone… For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller). Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely. In other demonstrations, they argued that a specific scenario seemed more likely because of representativeness, but each added detail would actually make the scenario less and less likely. In this way it could be similar to the misleading vividness or slippery slope fallacies. More recently Kahneman has argued that the conjunction fallacy is a type of extension neglect.”[1]
Notice that the fallacy assumes “independence”––that the probability of either condition occurring is unrelated to the presence of the other. Based on what we’ve been told, our minds trick us into believing that independence does not exist––that there has to be some (slightly) higher probability of her being active in the feminist movement. We draw these types of conclusions every day, instantaneously, not pausing to think whether they’re valid.
The conjunction fallacy mistakenly assumes a higher probability for an event occurring based on the erroneous belief that one fact necessarily implies a higher probability of another fact or set of facts occurring. Once this fallacy is kept in mind a truer picture of reality can be recognized. “Each added detail would actually make the scenario less and less likely”––our minds seem hardwired to assume precisely the opposite. By the way, “extension neglect” is “a type of cognitive bias that occurs when the mind tends to ignore the size of the set during an evaluation in which the size of the set is logically relevant.”[2]
For some this may seem somewhat counterintuitive. After all, collecting more bits of data––like points on a scatter plot––should improve our ability to draw correct inferences rather than make them less likely. Juror A, male, married, thirty-four years of age, a biochemist, works for a large drug company. We should pause before we draw any further conclusions. One answer to one question might change everything. The trick is to keep in mind that any inference we seek to draw has to be earned, not assumed. It’s almost as if you’re waiting for vapor to solidify into something a bit more tangible. The conjunction fallacy reminds us to be patient, open-minded––and not to reach our first conclusion until we’re sure the conclusion is in fact supported.
[1] Conjunction Fallacy—Wikipedia https://en.wikipedia.org/wiki/Conjunction_fallacy
[2] Extension Neglect––Wikipedia https://en.wikipedia.org/wiki/Extension_neglect
