Description: Similar to the conjunction fallacy, the disjunction fallacy occurs when one estimates a disjunctive statement (this or that) to be less probable than at least one of its component statements.
Disjunction X or Y (both taken together) is less likely than a constituent Y.
Mr. Pius goes to church every Sunday. He gets most of his information about religion from church and does not really read the Bible too much. Mr. Pius has a figurine of St. Mary at home. Last year, when he went to Rome, he toured the Vatican. From this information, Mr. Pius is more likely to be Catholic than a Catholic or a Muslim.
Explanation: This is incorrect. While it is very likely that Mr. Pius is Catholic based on the information, it is more likely that he is Catholic or Muslim.
Bill is 6’11” tall, thin, but muscular. We know he either is a pro basketball player or a jockey. We conclude that it is more probable that he is a pro basketball player than a pro basketball player or a jockey.
Explanation: This is incorrect. While it is very likely that Bill plays the B-ball, given that he would probably crush a horse, it is statistically more likely that he is either a pro basketball player or a jockey since that option includes the option of him being just a pro basketball player. Don’t let what seems like common sense fool you.
Exception: No exceptions due to basic probability.
What Now: Go back and read the entry for the conjunction fallacy again and make sure you know the difference.
Gilovich, T., Griffin, D., & Kahneman, D. (2002). Heuristics and Biases: The Psychology of Intuitive Judgment. Cambridge University Press.