The conjunction fallacy does not exist, as it claims to, for all X and all Y. That it does exist for specially chosen X, Y and context is incapable of reaching the stated conclusion that it exists for all X and Y.
But the research isn’t claiming that the conjunction fallacy exists for all X and Y. The claim, as I understand it, is that people rely on the representativeness heuristic, which is indeed useful in many contexts but which does not in general obey the probability-theoretic law that P(X&Y)<P(X).
Further evidence for the conjunction fallacy was covered on this site in the post “Conjunction Controversy”.
But the research isn’t claiming that the conjunction fallacy exists for all X and Y. The claim, as I understand it, is that people rely on the representativeness heuristic, which is indeed useful in many contexts but which does not in general obey the probability-theoretic law that P(X&Y)<P(X).
Further evidence for the conjunction fallacy was covered on this site in the post “Conjunction Controversy”.