Mind Teaser: Consider Linda
(I hope you enjoy this very revealing mind teaser!)
Please consider Linda, a 31-year-old woman, single and bright. When she was a student, both in high school and college, she was deeply concerned with discrimination and social justice, and also participated in anti-nuclear protests.
Which is more probable about Linda’s occupation today? (a) Linda is a bank teller; (b) Linda is a bank teller and active in the environmental movement.
Quick, what’s your answer? (a) or (b)?
—
If you answered (b), you are wrong, and in good company. That’s what most of my colleagues and I answered the first time we saw this teaser in one of our Stanford Organizational Behavior classes.
It is more probable that Linda is a bank teller, which is a whole category, that she is both a bank teller AND also active in the environmental movement, which is a subset of that whole category.
A recent Wall Street Journal article explains the phenomenon:
Free to Choose, But Often Wrong:
“When psychologists Daniel Kahneman and the late Amos Tversky conducted an experimental survey in the early 1980s asking people to answer this simple question, they discovered, to their surprise, that most respondents picked “b,” even though this was the narrower choice and hence the less likely one. It seems that saliency in this case, Linda’s passionate political profile trumps logic.”
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This isn’t entirely true.
I think the original researchers overlooked the fact that people would assume that the stated “feminist” clause in the second option implied that the first option did not include this eventuality.
It would be like asking whether you want an apple or an apple and a banana. Most people would assume that the first option does not include an banana. Very few people would ask whether I wanted an apple, and then give me an apple and also a banana.
So, according to most perceptions, the options are “bank teller and NOT IN the feminist movement” or “bank teller and IN the feminist movement”.
So it’s more that poor phrasing influenced logic.
I agree with Devin.
I agree with Devin too, but logic does not include assumptions. Therefore, strictly logically speaking, the answer would have been A. Which is easy enough to get if you’re thinking and on your toes, however most tests require ‘the best answer’ which would not be A. Who’s fault is it that we don’t get this right more often?
Malfist:
All logic includes assumptions; we call them axioms.
Language is very bad at representing logic in any form, so we’re forced to guess at the assumptions behind the alternatives we’re offered. Most of the time, the heuristic I mentioned above works for us.
I suspect you could unambiguously ask this question in a constructed language like Lojban, which is designed for that purpose. I wonder what people would say then?
I wonder how many people used the same “logic” I applied. If I say “banker”, I can be 100% right or wrong; if I say “banker” and “feminist” I have a chance to be 50% right if she is either one. I have two chances to get some part of the question correct based on a guess about occupation and potential feminist choices based on political activism at an earlier age. Does this make any sense?
Good discussion.
Malfist: exactly, “you’re thinking and on your toes” is another way of saying “you are fully engaged in rational decision-making”, not letting yourself be carried away by the phrasing of the question.
Devin: I agree that language is imperfect, and a formal logic representation of the problem would render the solution obvious. But I disagree with your conclusion. The problem is not language itself. Language is language. Language doesn’t have a brain. We do have a brain, and need to know how it works…including how not to be carried away by assumptions when we don’t want to.
Perhaps we should ask Linda about all this :-)
Davis:
well, your logic would be apt if second choice was ‘banker’ OR ‘feminist’ than ‘banker’ AND ‘feminist’. :-)
I’m back!
Alvaro: I believe that language is the problem. We do have the ability to interpret language, but we interpret it in a way that works most of the time. As I said, the heuristic I identified works most of the time with most normal communication.
The fact that the solution would be obvious if represented using another form of communication (perhaps a Venn diagram) means that the form of the question is the reason for the confusion, and not the logic itself. We simply don’t expect people to communicate in English the way this question is asked, and this is a reasonable expectation. Any ordinary English speaker would make the same conclusion about the apples and bananas.
The following XKCD comic sums up my view about this question:
http://xkcd.com/169/
Devin: You think people assumed the options were: “bank teller and NOT IN the feminist movement” OR “bank teller and IN the feminist movement”.
So people choose the second because OBVIOUSLY, the majority of the bank tellers of the world are feminists?
This is your argument to say that people are not stupid, it was just confusing language?
The claim that Linda is more likely to be a banker than a banker and a feminist is just unsubstantiated. Prima facie, an individual is more likely to be a member of a larger group than a smaller one, but that isn’t the judgement we are being asked to make. We’re given quite a lot of information about Linda’s political views and asked to decide whether she is an active feminist.
It’s more likely, prima facie, that I’m American than it is that I’m British, because there are more Americans than there are British. But if I say I live in the UK, think the Queen is great and call French Fries “chips” you would be foolish to say it wasn’t more likely I was British, despite the prior likelihood. In the same way, the fact that there are fewer feminist bankers than bankers is simply not the issue in Linda’s case.
Paul, it´s not me disagreeing with you, it is mathematics/ probability 101. As discussed above, we may be misled by language and our automatic assumptions, but that is precisely why this little teaser is eye-opening.
Once we are told that she is a banker, the probability of her being a banker: 100%
Probability she is, adittionally, active in the feminist movement: you pick. Perhaps 10%? 80%? in any case, it will be less than 100%, otherwise you are assuming it is impossible that she may have chosen not to be active in the feminist movement.
Perhaps people taking the survey associated the idea of feminism with being quizzed on being a “progressive” thinker and caught onto it like a buzz word. No longer does it become a question of AND/OR logic… no it just becomes a culture quite aware of how often it’s testing its ever-changing view on the ethical nature of the world.
I thought different from others, why would a bank teller and be active in the feminist movement. Does one exclude the other.
David Osborne probably described it best for me.
I remember one about a small older man who likes poetry and classical piano. Ivy League professor or truck driver? Well, obviously a truck driver, because they outnumber Ivy League professor several times over.
dwindle, not a very accurate analogy…
Do you think he’d more likely be a truck driver, or a truck driver who listens to Mozart all the time while mentally composing haikus?
or,
Do you think he’d be more likely to be an Ivy League professor, or an Ivy League professor who attends classical music performances every week?
The answer is (a). Linda is a bank teller “today”. She was an activist when she was a student. Do I know if she is still an activist today? Nope.
The answers very simple, it’s not that you’re “dumb”, it’s that people flip through sites like this one because theyre not worth thinking about. The internet is for entertainment, not for showing others the “ha ha boohoo” of how you fell for their little twist.
If the options were reverse (A. Linda is a feminist, and B. Linda is a feminist AND a banker) then most people would have chosen A. I guarantee it
I think what is more interesting is that people thought “Linda” ambitious enough to be both a full time banker and feminist. I love it!