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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, 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.


Kahneman, D. (2013). Thinking, Fast and Slow (1st edition). New York: Farrar, Straus and Giroux.

Registered User Comments

Sunday, April 15, 2018 - 12:11:27 PM
Is this a conjunction fallacy?

What is more likely to be true? Russia helped Trump to win the election without collusion or Russia helped Trump to win the election with collusion? I think that if someone said that collusion was more likely then that would be a fallacy of Conjunction.

Someone who believes that collusion took place would choose that option, but there is more evidence that Russia helped Trump than there is for there being collusion. I do believe there was collusion but I acknowledge that evidence for collusion is weaker than Russia helping without collusion. It is a fact that Russia helped Trump, but the question of collusion is murkier. Russia helping Trump without there being collusion is a larger set than Russia helping with collusion. Russia could help Trump to win with no collusion but not the reverse. It would not be possible for their to be collusion but Russia not help Trump to win. That would be like Trump asking Russia to help him and then they refuse. And if Russia does not help then there is no collusion.

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Bo Bennett, PhD
Sunday, April 15, 2018 - 12:30:06 PM
This is not the conjunction fallacy, however. To qualify for this fallacy, one of the conditions would have to be repeated. For example.

It is more probable that Russia helped Trump to win the election with collusion than it is Russia helped Trump to win the election.

Leaving out the "with collusion" part does not imply that it was without collusion; it just says nothing about collusion.

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