Conjunction Fallacy

(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, Y is more probable than X.

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:

Christianity is far more probable than just “some intelligent force in the universe”.

Explanation: Actually, that is not the case.  “Some intelligent force in the universe”, leaves it open for any God or no god, one god or multiple gods, gods that are beings, gods that are nature, with any name, and any property -- or just the property of intelligence and capablity of acting (force).  Christianity makes a very specific claim about the one and only God, with many properties and characteristics, whose name is YAWEH, and does not want us to eat shellfish.  Regardless of how much evidence there is for Christianity, it is far less probable than the probability that there is some intelligent force in the universe, since the Christian God is, “some intelligent force in the universe” plus many more properties.  With each property identified, the probability is reduced.

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

Mr. Pipp, is a sharp dresser, walks like a woman, talks in a very high voice, says “fabulous” way too much, and loves everything Barbara Streisand.  Is Mr. Pipp more likely to be a man or a gay man?

The way the question reads, there is a 100% chance Mr. Pipp is a man, and smaller chance that his is a gay man, because the group “man” includes all the members of the group “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.