In a way, this post is correct: the conjunction fallacy is not a cognitive bias. That is, thinking “X&Y is more likely than X” is not the actual mistake that people are making. The mistake people make, in the instances pointed out here, is that they compare probability using the representativeness heuristic—asking how much a hypothesis resembles existing data—rather than doing a Bayesian calculation.
However, we can’t directly test whether people are subject to this bias, because we don’t know how people arrive at their conclusions. The studies you point out try to assess the effect of the bias indirectly: they construct specific instances in which the representativeness heuristic would lead test subjects to the wrong answer, and observe that the subjects do actually get that wrong answer. This isn’t an ideal method, because there could be other explanations, but by conducting different such studies we can show that those other explanations are less likely.
But how do we construct situations with an obviously wrong answer? One way is to find a situation in which the representativeness heuristic leads to an answer with a clear logical flaw—a mathematical flaw. One such flaw is to assign a probability to the event X & Y greater than the probability of X. This logical error is known as the conjunction fallacy.
(Another solution to this problem, incidentally, is to frame experiments in terms of bets. Then, the wrong answer is clearly wrong because it results in the test subject losing money. Such experiments have also been done for the representativeness heuristic)
In a way, this post is correct: the conjunction fallacy is not a cognitive bias. That is, thinking “X&Y is more likely than X” is not the actual mistake that people are making. The mistake people make, in the instances pointed out here, is that they compare probability using the representativeness heuristic—asking how much a hypothesis resembles existing data—rather than doing a Bayesian calculation.
However, we can’t directly test whether people are subject to this bias, because we don’t know how people arrive at their conclusions. The studies you point out try to assess the effect of the bias indirectly: they construct specific instances in which the representativeness heuristic would lead test subjects to the wrong answer, and observe that the subjects do actually get that wrong answer. This isn’t an ideal method, because there could be other explanations, but by conducting different such studies we can show that those other explanations are less likely.
But how do we construct situations with an obviously wrong answer? One way is to find a situation in which the representativeness heuristic leads to an answer with a clear logical flaw—a mathematical flaw. One such flaw is to assign a probability to the event X & Y greater than the probability of X. This logical error is known as the conjunction fallacy.
(Another solution to this problem, incidentally, is to frame experiments in terms of bets. Then, the wrong answer is clearly wrong because it results in the test subject losing money. Such experiments have also been done for the representativeness heuristic)