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.Stephen J. GouldLinda 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.Suppose Björn Borg reaches the Wimbledon finals in 1981. Please rank order the following outcomes from most to least likely.Consider a regular six-sided dice with four green faces and two red faces. The dice will be rolled 20 times and the sequence of greens (G) and reds (R) will be recorded. You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you choose appears on successive rolls of the die.Consider another example: There are 100 persons who fit the description above (that is, Linda’s). How many of them are: 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. 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—formally, for two events A and B this inequality could be written as Pr ( A ∧ B ) ≤ Pr ( A ) {displaystyle Pr(Aland B)leq Pr(A)} and Pr ( A ∧ B ) ≤ Pr ( B ) {displaystyle Pr(Aland B)leq Pr(B)} . 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. In some experimental demonstrations, the conjoint option is evaluated separately from its basic option. In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without 'Linda is a bank teller' as an option). In this type of demonstration, different groups of subjects rank order Linda as a bank teller and active in the feminist movement more highly than Linda as a bank teller. Separate evaluation experiments preceded the earliest joint evaluation experiments, and Kahneman and Tversky were surprised when the effect was still observed under joint evaluation. In separate evaluation, the term conjunction effect may be preferred.