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Disjunction Fallacy

Description: Reasoning that it is more likely that a member is part of a subset rather than a member of the set which contains the subset.  This fallacy usually stems from thinking the choices are alternatives, rather than members of the same set.  The fallacy is further exacerbated by priming the audience with information leading them to choose the subset as the more probable alternative.

Logical Forms:

Event X is more likely than event X or Y.

 

Event Y is more likely than event X or Y.

Example #1:

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 Mulsim.

Example #2:

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: None.

References:

Gilovich, T., Griffin, D., & Kahneman, D. (2002). Heuristics and Biases: The Psychology of Intuitive Judgment. Cambridge University Press.



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