The Linda Problem

Logic Level 1

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 of the following scenarios is more probable?

This is a classic problem in experiments by Amos Tversky and Daniel Kahneman.

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

3 solutions

Guillermo Templado
Feb 12, 2016

If A and B are sets and A is contained in B, then the probability P(A) is less or equal to P(B)

Christopher Williams
Feb 3, 2016

Many people say that it is more probable that "Linda is a bank teller and is active in the feminist movement" In fact when Kahneman and Tversky tested this the majority chose this answer. Even though for Linda to be a bank teller and active in the feminist movement, she must be a conjunction of two things (a bank teller + active in the feminist movement) which is less likely than just of the things being true. It is more probable that Linda is a bank teller.

but in this case there would be things that would be indicative of her being apart of the feminists group so that would make it more likely? Actually i think i see your point, either she is a bank teller which she is or she is a bank teller AND a feminist which she might not be, right?

Tim Andrews - 5 years, 4 months ago

I think you're arriving at the correct answer, and Guillermo's solution is helpful here. Set $B$ , that she is a bank teller, contains set $A$ , that she is a bank teller AND active in the feminist movement. It also contains that she is a bank teller and not active in the feminist movement. Or that she is a bank teller and loves donuts. It contains a larger set of probabilities than the set $A$ that she is a bank teller and active in the feminist movement. $P(B) > P(A)$ . The description of Linda makes us think that she's likely to be a feminist, but logically a conjunction of two events is less probable that just one of those events occurring.

In Daniel Kahneman's book, "Thinking, Fast and Slow", he mentioned that Stephen Jay Gould tried this same problem and wrote that, although he knew the correct answer, "a little homunculus in my head continues to jump up and down, shouting at me - 'but she can't just be a bank teller; read the description'"

Christopher Williams - 5 years, 4 months ago

What if you look at them as completely separate answers though. You are saying that A is a subset of B, but I was looking at them as 2 completely separate situations. Answer A, has very little probability because in the description there is very little to insinuate that she would be a bank teller. In answer B, the likelihood of this person meeting the second criteria is higher, and therefore raises the probability of the overall answer. Being a bank teller wouldn't affect the probability in any way.

Sean Davis - 5 years, 3 months ago

@Sean Davis – The question is tricky in this regard, it makes you want to think that Linda is active in the feminist movement and therefore choose the answer that includes this because you see that component of the answer as being more probable. If the question was is she a bank teller or active in the feminist movement then that reasoning would come into play. However, the problem says bank teller and active in the feminist movement.

Consider ignoring the description of Linda. If you know nothing about her, which is more likely? That she is a bank teller or that she is a bank teller and active in the feminist movement?

Or consider another similar problem, you see a male stranger walking down the street, is it more likely that 1) his first name is Bob or 2) that his first name is Bob and his last name is AwesomePossum? While I really want to pick 2, and hope that someone has that last name, I know that the set of people with the name Bob is far greater than the set of the people with the name Bob AwesomePossum. I also know, that if a stranger's name is Bob AwesomePossum, that their first name would be Bob, which is to say that the set of every stranger whose first name was Bob contains the set of every stranger whose first name is Bob and whose last name is AweseomePossum.

Even though Bob AwesomePossum is cool name, out of all the strangers out there, more of them are going to be named Bob than Bob AwesomePossum. That's intuitive.

To connect the two, if you eliminate the description, it becomes easy to see that Linda is more likely to just be a bank teller than to be a bank teller and active in the feminist movement. Adding in the description doesn't change the probability of the situation, it just makes you, because of cognitive bias that is a part of all of us, want to pick the choice where she is active in the feminist movement. Just like I want a stranger walking by me to be named Bob AwesomePossum, even though I know it is more likely just that his first name is Bob than both his first name is Bob and last name is AwesomePossum.

Christopher Williams - 5 years, 3 months ago

@Christopher Williams – Here's another way to look at it. If you read the description and think that Linda is very likely to be active in the feminist movement, "Linda is a bank teller" is obviously correct if "Linda is a bank teller and is active in the feminist movement" is correct. But it doesn't work that way in reverse. "Linda is a bank teller" and "Linda is a bank teller and is active in the feminist movement" are equally likely only if it is 100% certain that Linda is active in the feminist movement. From the description, she sure seems likely to be active in it. But what if she's a single Mom with four kids, works a second job in addition to her bank-teller job, and just doesn't have any time to be active in anything else besides work and raising her kids? Or what if something happened to her after college that changed her outlook on the world and she no longer feels the way she did in college. Since it goes too far to say, based on a three-sentence description, that Linda is 100% likely to be active in the feminist movement, it is therefore true that "Linda is a bank teller" is more probable than "Linda is a bank teller and is active in the feminist movement."

Jay Cooper - 4 years, 3 months ago

Though there is information that suggests that Linda is in the feminist movement, there are still a VAST majority of possibilities where Linda is a bank teller, rather than both.

Aaren Ruparel - 3 weeks, 1 day ago

Dag Bøye
Feb 3, 2017

A (bank teller) is undetermined from what we know.
B (feminist) is probable from what we know.
P(A) is still more probable than P(A) AND P(B).

The Linda Problem

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