# How you can avoid committing the "conjunction fallacy"

Originally published at: http://boingboing.net/2016/08/25/how-you-can-avoid-committing-t.html

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“Is a bank teller and feminist” makes more sense as a function of narrative logic, whereas “is a bank teller” makes more sense as a function of basic probability.

Guess which one of those capacities human beings use to navigate their social graph? Socializing is probably the most computationally complex thing that human beings do. It’s not really terribly surprising that’s what most of us are optimized for.

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Because “AND” means “MULTIPLY” when it comes to combining probabilities, so the more things you ‘AND,’ the less likely it becomes.

Although when things are not independent…

The odds on a president being rich AND white AND male, for example…

Guess I have to listen to the podcast.

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Conjunction junction, what’s your function?..

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How you can avoid committing the “conjunction fallacy”

Look, conjunction fallacy happens to everyone now and again. I still love you, and I still think you’re sexy. I’ve just been under a lot of pressure at work this week, and have stuff on my mind. I’m really sorry honey. Why don’t you just lay back an let me give you some ignoratio elenchi?

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I tend to favor the use of probabilities, because they seem most likely (probable?) to relate to real-world phenomena, whereas narratives nearly always depend upon stereotyping of scenarios and relationships.

Of course it takes a lot of resources to attempt to model something which is basically arbitrary, but I think it can also easily be argued that this is not effective use of cognitive resources. I prefer to socialize based upon explicit communication, and avoid relationships based upon excessive guesswork.

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Because while the paragraph supports the idea that she’s a feminist it doesn’t say anything about bank-telling. Therefore the chance of her being a bank teller is unknown: say 50%, and while the chance of her being a feminist appears high (say, 80%) the cumulative likelihood of both bank-telling and feminism being components of her life has to be lower than that of either on their own.

The manner of the question of leading, though; it’s deliberately structured in a way that leads the audience to presume that the bank-telling component is true.

I guess I am so smart, after all.

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You really need that much info to explain why people get this wrong? I mean the answer is obvious but then again I spend a lot of time writing code that relies on boolean logic so it the correct answer is simple.

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But not so fast!

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This is bullshit.

A logician wrote a question like this: Which is more likely: A or (A AND B)?

In common language (not logic) that question will be interpreted by many people as “(A AND ~B) or (A AND B)”, and fairly answered the former.

The question is tricking people.

If you asked the question fairly, in a way they could understand, and said, “Which is more likely, that she is a bank teller and is either a feminist or not; or that she is a bank teller and a feminist” that is, if you were explicit about what you were asking, you wouldn’t catch so many people.

I believe there is an xkcd for that:

Maybe the episode goes deeper into how this mistake of thinking affects people in their daily lives. But the “people got this question wrong” thing is just smugness.

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It was also put out in June. The latest episode is an interview with Dean Burnett, author of Idiot Brain.

Is BB screwing up the updates for this podcast, or is it something YANSS is dropping the ball on?

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or equal to

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What does the use of probabilities say about the likelihood of interacting with someone who thinks in terms of probabilities versus interacting with someone who thinks in terms of narratives?

I should definitely have used “most humans” or “tend to” somewhere in there, though. Thanks for calling it out.

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Hey Joe, what do ya know?

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Only if there is more than one of Linda. As long as there is only one of Linda, there is no such thing as a probability for what she is. Which is to say that probability only has meaning when there is more than one example of an outcome. When you flip a coin once, you don’t have an even chance of getting heads or tails, you have an absolute chance of getting the one and only outcome you get. You have to flip the coin at least twice to show a probabilistic distribution.

Understand that my critique is not of the conjunction fallacy itself. That is quite real. But the example of a single individual having a probability is itself a fallacy and not an accurate example of this fallacy. I wouldn’t mention it if it were just this show’s example, but Linda is the classic example of the conjunction fallacy and in fact she is not, by herself, an example of it.

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That’s exactly what they said! That’s truly remarkable!!!
Where ever did you come to such a conclusion ?

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You’re making it sound like the question’s wording is designed to trick people into committing a logical fallacy that they wouldn’t otherwise make in their everyday lives, but this isn’t true. People make this fallacy all the time, and this question is simply designed to demonstrate the fallacy in a setting where the right answer is definitely known.

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This fallacy occurs because people are basically answering a different question than what was asked. Instead of answering a question about two probabilities, they’re answering a question about two ratios of probabilities:

1. P(Linda is a bank teller) / P(randomly selected person is a bank teller)
2. P(Linda is a feminist bank teller) / P(randomly selected person is a feminist bank teller)

In this case, ratio 2 is most likely the larger quantity, because compared to ratio 1, ratio 2 likely has a slightly smaller numerator but a much smaller denominator, leading to an overall larger ratio. On the other hand, if bank tellers as a group just happen to be overwhelmingly feminist, ratio 1 might actually be larger.

Regardless, this is still a fallacy, because people will determine the answer to the question as I’ve described it but then act as if it were the answer to the original question, which is very much is not.

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Public schools should require study of cognitive biases. Maybe with some sort of violent punishment game ala the XKCD comic above.

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After lurking for 10 years I signed up, just now, to say THANK YOU

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