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Conjunction Fallacy

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(also known as: conjunction effect)

Description: The assumption that more specific conditions are more probable than general ones.  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 option.

Logical Form:

X is a subset of Y.

Therefore, X is more probable than Y.

Example #1:

While jogging around the neighborhood, you are more likely to get bitten by someone’s pet dog, than by any member of the canine species.

Explanation: Actually, that is not the case.  “Someone’s pet dog”, assuming a real dog and not some robot dog, would also be a member of the canine species.  Therefore, the canine species includes wolves,  coyotes, as well as your neighbor’s shih tzu, who is likely to bite you just because he’s pissed for being so small.

Example #2:

Mr. Pipp, is a sharp dresser, too good-looking, works as an interior decorator, and loves everything Barbra Streisand.  Is Mr. Pipp more likely to be a man, or a gay man?

Explanation: It would be fallacious to say that Mr. Pipp is more likely to be a gay man—even if we found out that Mr. Pipp worked nights as a dancer at a drag queen show.  There is a 100% chance Mr. Pipp is a man, and a smaller chance that he is a gay man, because the group “man” includes all the members of the group “gay man”.

Exception: When contradicting conditions are implied, but incorrectly stated.

In the example above, the way the question reads, we now know that there is a 100% chance Mr. Pipp is a man, and a smaller chance that he is a gay man.  However, if the questioner meant to imply, “straight man” or “gay man” as the choices, then it could be more of a poorly phrased question than a fallacy.



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