Logical Fallacy: Conjunction Fallacy

The 'conjunction fallacy' is the assumption that conjoined circumstance are more probable than a single. Single is always more probable that multiple.

Here's the break-down:

(a) When there are common elements in a in scenario with multiple options, 

(b) an additional element reduces the probability of occurrence.

(c) Therefore, x is alway more probable than x+y.

Examples:

1. The Linda Problem

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.

2. Linda is a bank teller and is active in the feminist movement.*

You most likely picked number 2. This is wrong. Both options involve Linda being a bank teller, however, the second options adds another layer of probability. To explain it in another way, let’s reverse the situation.

Which is more probable?

1. Linda is in a feminist movement.

2. Linda is in a feminist movement and a bank tellers.

Again, option one is the right answer, as the probability of Linda being a bank teller adds an additional probability on top of her being a feminist.

2. Sam Harris v Cenk Uygur

The following is a great example of the conjunction fallacy in a real argument. Once you learn the Conjunction fallacy, watching Cenk in this video is very cringeworthy. The lesson here is that it’s crucial to know logical fallacies.

When Sam comments, 'this is a cute statement', he realises that Cenk just committed the conjunction fallacy. 

The video will automatically play from the correct position. If not, watch from 17:33 to 19:13.

3. The Dog and the Canine Species

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.

The above statement is clearly absurd. It does however demonstrate the faulty logic. Now, the 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. **

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Sources:

*Judgment Under Uncertainty: Heuristics and Biases by Daniel Kahneman, Paul Slovic, Amos Tversky

**Logically Fallacious: The Ultimate Collection of Over 300 Logical Fallacies by Bo Bennett, PhD

Categorisation: philosophy → logic → logical fallacies → formal

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