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?
Note: Please answer BEFORE checking the comments.
Comments: Spoilers completely permitted.
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So what are you trying to judge here? I kind of feel liek my answer should be "Fuck.. I don't know."
ReplyDeleteThis is a question from a famous cognitive psychology experiment. I imagine he'll do a follow-up post later providing some explanation.
ReplyDeleteEdit: whoops, I see spoilers are permitted! The correct answer is that there is a higher probability she is just a bank teller because it's a less restrictive answer. But there are lots of cues in the question priming you towards answer B - even though answer A includes everything in answer B, plus more, making it more likely.
P(bank teller ∩ feminist) = P(bank teller) * P(feminist) or something like that.
ReplyDeleteAh, I see... so yes, I answered wrong then.
ReplyDeleteI think the results thus far show that the majority of people Will knows are familiar with this being a trick question (likely due to this questions fame in demonstrating how heuristics fail)
ReplyDeleteIt's weird that our minds assume that the 2nd option means "that she is a feminist assuming you already know she's a bank teller"
ReplyDeleteI read the question as, "Linda has a particular job and either is or isn't a feminist." She has to be a bank teller, as "Linda is not a bank teller" isn't an option, so socially, you'd assume that a good faith asker of the question is stipulating that she is a bank teller. Thus, I just ignored that part of the answer and focused on whether I thought she was a feminist.
ReplyDeleteNote: I'd probably answer the question differently in the context of a math class about probability than a psychology class; in the latter, I feel like it's more about the cleverness of how the question is phrased, rather than actually saying anything about the answers. Or to put it another way, if you expected that people asked that question in a neutral context would not expect it to be about absolute probability, in spite of the question, "which is more probable," you'd be right.
David Rothfeder let's talk about this from a semantics-and-pragmatics point of view, eh? Like, the "correct" answer assumes a very particular set of interpretive rules, which don't really apply to casual conversation. This isn't casual conversation and there's no other good interpretation here, but it's easy to see that people interpret this differently "in the wild".
ReplyDeleteDavid Rothfeder : So, in a job interview years and years back, someone asked me “so why are Man-hole covers round.” I said “I don’t know the history for sure, it could easily be some contingent fact of past circumstance, but I’ll note that a circle is the only shape that you can’t rotate the man-hole cover somehow and make it fall through its hole onto someone below.” The interviewer disappointedly said “Oh, so you’ve already heard that question.” I did not take that job.
ReplyDeleteIt’s possible that people have heard this question before, but it’s also possible that some people are grounded enough in what probability actually means that they can figure it out prior to being exposed to the anecdote.
Rabbit Stoddard : That’s cognitive bias, not a difference of conversational styles. It will lead you to wrong answers, when presented with questions in this format. Since people who benefit from you getting the wrong answer deliberately frame things in this way, it’s pretty important for folks who get tripped up by that framing to make a deliberate effort to be aware of it. I worry at any response that says “Well, it’s about how you asked the question,” because it sounds like not recognizing that problem, and without recognizing it you can’t work on it.
ReplyDeleteLinda is a bank teller
ReplyDeleteLinda is a bank teller
Linda is a bank teller now
youtube.com - Ramones - "Sheena Is A Punk Rocker" (Official Music Video)
Tony Lower-Basch Try that a different way.
ReplyDeleteWilliam Nichols : Fair enough. Editing.
ReplyDeleteTony Lower-Basch I'm not actually suggesting it's a difference in conversation styles. I'm noting that my assumption about what the question was was, in fact wrong- thus I was tricked by the trick question, and further explaining what I assumed, and why.
ReplyDeleteWhich may be uncovering a specific cognitive bias, but damned if I can figure which one. Other than, "I wrongly assumed I knew what the question was asking, reduced the possible answers to the value that seemed unknown, and guessed based on evidence that was not actually important to the actual question being asked."
One of these is a strict subset of the other in logical terms — but there’s a semantic issue.
ReplyDeleteWhen you offer these two options, I attempt to contrast them based on context.
That means I have two possible interpretations, in context, of “Linda is a bank teller.”
A) Linda is a bank teller, and could be a feminist or not. (Strict reading in isolation)
Or
B) Linda is a bank teller and NOT a feminist (based on contrast with the other stated option)
Similar semantic twist — if I offer you a BLT or something in a wrap, does that mean a BLT is a wrap is an option or not? Would you have to ask a clarifying question?
So, what even IS this?
ReplyDeleteThis is the "Linda Problem", demonstrated in a lot of phil courses. When first running across it, I made the cognitive error because of course Linda is a feminist. Pfffft.
[ And, well 90% * p(bank teller) is always less than p (bank teller) ]
As of now, only 30% of you have made that same cognitive error. That's really good!
And yes, there are clues that lead you to believe the other. To make you misinterpret the question. It's a bit of a trick, but a good one to point out specific types of cognitive errors -- which we all make.
Why I brought this up: There was a recent 538 article with a headline along the lines of "democrats don't know republicans. Republicans don't know Democrats" and, well, I thought they got it wrong.
Instead, my conjecture is that we are bad at conditional probability, and that is largely what they were seeing. I think 538 overfit the results -- this being the most common statistical sin.
I'm going to continue to read the discussion, which is fascinating.
The cognitive problem is really quite potent when chained. Two days ago I was chatting with folks who casually chained “immigrants are coming from South America, they don’t speak English, they’re poor, they’ve been exposed to a lot of violence, it’s no wonder (offensive stereotype that after this chain of unconscious limits to the group they’re thinking about, they imagine now seems likely in context)”
ReplyDeleteWhat is more likely? That a person is an immigrant, or that a person is an immigrant from South America?
Note: William Nichols - I agree that we are bad at conditional probability, and also at large numbers. But also am saying that "how many republicans are $demographic" and "how many $demographic are republicans" are two different questions with answers that are useful for different rhetorical reasons.
ReplyDelete"how many republicans are $demographic" is useful for reminding one of the real numbers involved, and putting one in mind of the percentage of people on the whole who are $demographic, while showing that people are not good at grappling with those numbers.
"how many $demographic are republicans" is useful for figuring things like, "what is the importance of this party affiliation to this demographic," "what does this tell me about people in this group as a whole and their party affiliation?" But it's harder to make a point about numbers with that question, unless the numbers are within the middle 50%, and are perceived to be outside of that bound. Or vice versa, I guess.
So... yes? I don't think they're necessarily wrong, but yeah, there's a reasonable chance that the respondents heard the one question as the other? And it depends on what point they wanted to make? And the study would be more interesting and useful on the whole if they asked both questions?
Tony Lower-Basch
ReplyDeleteOoh, that’s a good one.
Trump’s comment about people being animals — was he referring to Hispanic immigrants, or members of MS-13?
If he’s referring to immigrants, that’s a known issue.
But if he’s referring to MS-13, it brings up this bias. I think he believes migrants from South America are overwhelmingly MS-13. Except for a few, who he assumes may be good people.
So we move from the general to the specific — migrants to MS-13 — and then come up with a not-absurd rhetoric and plan. Then we apply the plan, which might make sense if applied to MS-13 members, to everybody who might look a little like an MS-13 member. And what the hell. And then this view spreads through conservative media, that you can’t tell a toddler from a gang member so you need to treat them all like gang members.
That’s probably giving to much credit to his incompetence — I’m entirely clear Sessions had this all planned out.
I had to revise my vote because of the typo :-P
ReplyDeleteFemmnist. Oops.
ReplyDeleteUpon further thinking (and w/o reading comments):
ReplyDeleteProbability of (a) should be higher than probability of (a AND b), or? So I was wrong anyway.
Indeed, it mostly does not matter what the second thing is.
ReplyDeleteAh I read the two options as being complementary, whereas one set contains the other
ReplyDeleteLisa is a woman who has aged past the "tee hee I'm not like other girls" phase and is realizing she's underpaid as a bank teller compared to her male counterparts. Hence: feminist.
ReplyDeleteYou ok, Lex Larson?
ReplyDeleteWilliam Nichols Yeah, I just know this question was probably (har har) written by a man who didn't think about human factors before making a woman's belief in her own humanity a logic problem.
ReplyDeleteLex Larson I'll take some of the blame for that: The original is "Linda is a bank teller and is active in the feminist movement.", but I ran out of space in the answer slot.
ReplyDeleteBut, agreed: Tversky and Kahneman are dudes and it shows.
How can one tell whether the set of answers implies that the first should be read "Linda is a bank teller and we say nothing about her being or not a feminist" or "Linda is a bank teller and not a feminist"?
ReplyDeleteAlso, while on the unsaid scale, aren't the probabilities of her being a bank teller rather low, and hence both answers wrong? Or are the "answers" actually giving things that should be in the wording?
Also, is this a lesson in probabilities or in rethorics?
Gherhartd Sildoenfein the set of bank tellers is larger than the set of feminist bank tellers by definition. All it takes is a bank teller not being feminist to make it larger. Therefore just being a bank teller is a higher probability event.
ReplyDeleteThe story about Linda is a red herring to misdirected us into thinking that the first question implies the bank teller not being a feminist, which is not the case
I get that, Ivan Vaghi , but this rests on "how do I fill in what is implied", which depends on the context. This set reasoning is "the correct answer" in mathematics/probabilities, but is it absolutely? Should it be?
ReplyDeleteGherhartd Sildoenfein : Speaking of rhetoric and the implication of things unsaid... you are raising the same class of question repeatedly, without making any affirmative statement yourself. It’s all questions. That could be taken to imply (while leaving it unsaid) that you think there is an important argument that those questions highlight. Rhetorically, it could even imply something about the argument you imagine.
ReplyDeleteBut you haven’t said any of it.
Could I ask you to expand on your thinking in the affirmative?
Yeah, of course, and I will as soon as I am in front of a real keyboard.
ReplyDeleteI'll be honest I think this is a badly framed question at best, or a trick question at worst. The second answer strongly implies that the first answer is "Bank Teller, not Feminist". If it's not true than your possible answers are basically. 'Some people' or 'anybody'.
ReplyDeleteIf it's a trick question, that's fine. It's tricky.
If the question aims to achieve anything aside from tricking the taker, then it's poorly formatted. A biased question if you will.
Yanni Cooper It is not that the question is poorly framed, it is a very simple question. It is designed to show off the flaws of our heuristics in judgment calls by showing that people assume ideas to be there that are not in the text at all. Which is more likely L=a or L=a and b. Humans are often caught up in narratives that are not based in fact. This is a characteristic of humans that was not well represented in economics, so these guys tried to find a way to put these counterfactual thoughts on display, to be examined for why/when they occur and how to counteract them.
ReplyDeleteDianne Harris So you're saying it's a trick question?
ReplyDeleteYanni Cooper Before you get into a fight with Dianne Harris, let me recommend a reading list:
ReplyDelete-- The wikipedia page on the conjunction fallacy
-- Freakonomics
-- As much planet money as you can stomach. For me, this is "very little", but I dislike podcasts-
-- Nudge
-- Predictably Irrational
-- Thinking Fast and Slow
I don't want you fighting above your weight class. This is a woman who argues with economists and, more often than not, wins.
It is indeed a poorly framed question, because they chose to use a woman teller and feminism (the assertion women are people) and not, say, dogs and dogs liking hot dogs.
ReplyDeleteThese two men COULD have used anything except gender and feminism, but they didn't. They specifically chose gender and support of feminism as their cute little 'thought experiment' -- without regard to the real-world experiences of, y'know, actual women and actual feminists.
I'd prefer if my logic problems, didn't reinforce bias, especially when they're attempting (however poorly) to expose a form of bias.
Sure. If that helps you. It's a trick question.
ReplyDelete“Tricky” is an interesting word, in that it can either imply “this is intended to be deceptive” (as in “he tricked me into thinking I owed more money than I did!”) or imply “this is complicated or difficult” (as in “be careful coming down that slope, the footing is a little tricky”).
ReplyDeleteFWIW I'm not really trying to start a fight on the internet! It seems to me that the question poses as a demographics question, but actually it's a math question.
ReplyDeleteMaybe I'm just trying to justify why I got it wrong. Or maybe I have a long, and deep seated resentment towards poorly written tests. Or maybe it's that I'm a programmer.
Tony Lower-Basch I mean, it could also be both!
ReplyDeleteOk, I finally have a proper keyboard under my fingers, here we go Tony Lower-Basch.
ReplyDeleteI am mostly asking questions, because that’s how I am thinking. I have some hypothesis and guesses, but nothing definitive. Of course, some conjectures support my questions, and I can express them in a more affirmative form.
I find (I wonder if) this “test” (is) dishonest, a bit like some kids jokes. Like the author trying to lead us to think they are speaking about one thing and testing if we catch they are in reality speaking about something else and chekcs whether we can catch that they are trying to pull one on us. Being smart enough to catch this mood, I am faced with three possibilities:
- Playing smart aleck and choose the opposite answer to the instinctive one;
- Want to finish this as soon as possible, and give the asker some satisfaction and choose the instinctive answer, let’s get done with this;
- Analyze to see where the trick is and give the correct answer with the correct explanation.
All in all, I guess the “test” doesn’t prove anything much, except the test’s author trying to be a smart ass. (Now I might be totally mistaken by not knowing in what context the original problem is presented.)
And how does this works? This is what I surmise:
The problem’s data leads the reader to believe it is talking maybe about sociology or psychology, or just plain every day conversation. Context determine how we parse the text, notably how things are implied. There is an innocent looking (and purposefully too discreet) context-switch in the form of the question and of the answers: “which is more probable”, which will be ground for claiming that we were talking mathematical probabilities, exam-question style, from the beginning.
In a non-mathematical context, the data, question and answers say: “given that 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. Now she is a bank teller. Is it more probable that she is a feminist, or not?” It is asking if, for the reader, there is a clear correlation between these traits and a feminism. Not if the probability of two events occurring together is equal or less to the probability of only one of those occurring.
Now, I have no doubts that many people will make the "shown" mistake in situations where it matters, we are, as a people, not very good and not very educated to avoid this error. But to me, all this test probably prove, is that yes, it is possible to write ambiguous questions.
But all this leaves me with my root question: why do some people insist that the strict mathematical interpretation is the only correct one?
ReplyDeleteGherhartd Sildoenfein : So if I understand you rightly, you feel that in a non-mathematical context it is clear that there is a question that is being implied (“do these traits correlate with feminism?”) and that the correct answer to the implied question is as valid as the correct answer to the actual question. Have I understood?
ReplyDeleteI have some questions also. Why do some people assume bad intent, or poorly designed sentence structure, instead of human fallibility? Which is more likely? Why do people, who do not have PHD is psychology and a Nobel prize, assume they know more about the field of behavioral economics than those who do? Why are some people so insecure about about their mental capabilities that they take a demonstration of humanity as a personal attack?
ReplyDeleteTony Lower-Basch more or less. Less because you reframe it in a clearly scientific-logicial-strict-interpretation language. While the "validity" of the interpretation and of the answer depend on context. As I do not have a "real" context, I can't know, and in this context here, I have no element to help me determine whether one way is preferable to the other.
ReplyDeleteTo me, in this case, observing that most people "don't answer correctly" reveals a failure of communication more then a shortcoming of the audience.
Dianne Harris I don't follow everything you write here. I am not sure to what parts of this conversation this applies to. I am interested in knowing more, would you explain?
Gherhartd Sildoenfein : I agree that it is more probable that "banker and feminist" responses result from a failure of communication than that they result from a failure of communication due (in part) to a cognitive bias in the audience. But I do, in fact, think that it is very often both: Human beings are prone to fill in these specific types of information-gaps in the way you describe: Given two options that are "1. You know A," and "2. You know A and B," many (I suspect "most") people will revise option #1 to be mutually exclusive with option #2, in order to create a collectively exhaustive set of categories, where no single case fits into either more or less than one category. We just like mutually-exclusive-collectively-exhaustive categorizations.
ReplyDeleteThe OP question (by design) highlights that propensity, but does not create it. Do you agree?
Unreservedly.
ReplyDeleteGherhartd Sildoenfein : So, as William has pointed out elsewhere ... this gives us a chance to choose between (1) practicing introspection about how our mental systems are vulnerable to manipulation, or (2) treating the question as if it were the source of error, and not then introspecting.
ReplyDeleteI'd suggest #1, but I can't force anyone to anything.
So the problem is an icebreaker for an education effort. That is context.
ReplyDeleteGherhartd Sildoenfein : I don’t know about education (at least in the didactic sense).
ReplyDeleteEvery error is an icebreaker for introspection. I thought that context was universal.