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Philosophy experiment Answered

I came across an experiment in a text on the Philosophy of Science, and I would like to test the results, if I may.

Consider this scenario:

Linda is is 31 years old, single, outspoken and very bright. She majored in philosophy (it's an American text).

As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-war demonstrations.

Given this background, which of these statements do you consider to be the most probable? You do not have to justify your statement (though you may if you wish), simply post the letter of the most probable statement:

a) Linda is a teacher in a primary school.
b) Linda works in a bookshop, and takes Yoga classes.
c) Linda is active in the feminist movement
d) Linda is a psychiatric social worker.
e) Linda is a member of the League of Women Voters
f) Linda is a bank clerk
g) Linda is an insurance salesperson
h) Linda is a bank clerk, and active in the feminist movement.

If you are feeling particularly helpful, you could rank the statements in order of probability (most likely to least likely).

Thank you in advance.


Update: The answers:

There isn't a "right" answer.

The point is that (h) was consistently given a higher average probability than either (c) or (f).  There was no statistical difference between the results of a group of undergrads with no training in statistics, students who had taken basic courses in probability as part of their main subject (eg medicine) or even graduates of Stanford Business School who had taken courses in advanced probability and statistics.


"Dave" studied History at University, he's not married, and doesn't own his own house. He likes to socialise in the pub with friends.

a) Is a local councillor, and has a Financial day-job
b) Works for his girl-friend's internet business and likes getting trashed on drink & drugs
c) Lives with his mum and works for an insurance company
d) Has dreams of going to Iraq as private-sector security, but is temp-ing (still)
e) Want's to be a Town-Planner and has moved to London to study at Kingston.



And Dave spends too much time on Instructables as "lemonie". LOL

Actually they're all correct (5 different people).



what happens know ?
is there a right answer ?

You have "h" twice, and "g" not at all.  Could you repost with those corrections?

sorry, the 2nd h was supposed to be a g


There ya go :D

Okay, thanks!  And now that other people have talked about it, I can point out the (only) error in your analysis. 

Since "h" is the composition of two different items (specifically, h = f AND c, the probability that h is true must be less than or equal to the separate probabilities that f is true, or that c is true.  Therefore, h must appear below both f and c in any correct list of probabilities.

Mathematically, P(h) = P(f&c) <= P(f)*P(c).  The equality holds only for the case where either P(f) = 1 or P(c) = 1.  This is just because probabilities are normalized such that 0 <= P(x) <= 1.

Well in my opinion H would be more likely as a combination as it relates to two of her qualities, F alone would be to plain and not satisfy the feminist thing, C alone would not utilize her brainpower. So H would appear above both F and C.

Which is the point of the whole thing - even suitably-trained people tend to ignore probabilities when making snap decisions.

I know of a few people, they consider themselves suitably trained, and will overanalyze and use probabilities in their snap decisions, and thus my observation, do not have common sense.  My snap decisions are based on experiences and gut feeling.  In trying to answer this question, I was biased on real world "stereotypes" instead of probabilities.

I'll update the OP when I have more responses.

I'm not very philisophical, but, I choose c. I believe if she has that major in philosphy, then she wouldn't be in a bookshop, so I would have chosen b otherwise.

No reason. Gut feeling.

" She majored in philosophy " wouldn't that mean she works at starbucks or McDonalds? what else can you do with a philosophy degree?

That's weird, as I posted that, if anything, she could NOT be F or H   LOL

banks in our country hire people that do NOT think for themselves, for the most part, but will follow a strick set of simple rules.   :-)   That's not the Linda described in the beginning.

I remember this riddle from Logic class at CTY...
I can't seem to remember the answer though.

P(A&B) <= P(A) and P(A&B) <= P(B) for all A, B, P.


Don't try to think on an empty stomach.

Psst, he forgot the jelly.....I think he might just be in a jam....

.  B is the only statement that is true. Possibly E is true, but I doubt it.

How do you conclude that b is true?


"You do not have to justify your statement..." ;)

No, but I'm interested. You do not have to withhold your reasoning?


.  It just felt right. No particular reason(s). ;)

As a merry can, you can plead the 5th, your right to bear arms guarantees it.

I think b fits the description of Jessyratfink and for all else there is Lithium Rain.

I say C ( I read the update)

I think C because she is 31 and single, worried about discrimination and social justice (Being a women maybe?) So this makes me think that she is a feminist. The reason I don't think F is because the text doesn't support her being a banker or not.

I wouldn't draw any relationship between the description and a-h.
I then discover that this is popular as an example of "conjunction fallacy", "Pirates prevent global warming" being a more amusing one.


You're right about conjunctions being involved, and the ability to do relative rankings is part of that.  However, Kiteman is correct that it is an exercise in how people infer unknowns based on experience and known category membership.

No, I've encountered this exact example, possibly in a Michael Shermer article, but certainly in an analysis of how badly people deal with joint probabilities.

If we continue this discussion, though, we're going to give away the point.

Correction, and thanks to GMoon, it was in a Stephen J. Gould essay, not Shermer.   GMoon also, unfortunately, revealed the point.

I got it from Science: Key Concepts in Philosophy by Steven French.

OK - I get your position - thanks.


Nope.  It's an experiment in heuristics.

Thanks, but I wasn't asserting an opinion as to what you were doing with this - just an observation.


It was a tough choice, but E is what I'd go with. My first instinct was A.

I'd have to go with LR on this one.  I see no information relative to any of the final choices.  I mean, I personally know of a few women that were "active" demonstrators for equal rights, but that now consider some portions of the feminist movement (as with many such things) has gone beyond equality and are seeking advantage (in some areas).  So, one can not infer c  e nor h.  If anything,  I would only think that (possibly) Linda is NOT a bank clerk (if the context of this is in the USA)   :-) 

I'm not being *purposefully* perverse (or attempting to be "better than all you yuks making assumptions" or something like that), but honestly none of them seem very much more likely than the others. >shrug<


8 years ago

I'll vote a, f, e, g, d, c, h, b -- based mostly on my guesses as the # of people employed in each field...

Don't read the following (if you don't want to be influenced...)

Years ago I heard Stephen J. Gould speak about a similar experiment that was conducted on grad students. Simple set theory automatically eliminates answers with more than one option--it's statistically impossible for someone to have a higher probability of multiple characteristics over a single characteristic. At best, the sets are congruent (or one set is completely enclosed within the others.)

Multiple sets are ANDed-- statement H is true only if Linda meets two criterion, rather than one, so the statement is true only where the sets overlap. Picking the larger of the individual sets will be a higher probability than both.

PKM alluded to this, too. BTW, in Gould's experiment, most grad students failed, and picked the multiple options...

Actually, I should not have written automatically eliminates, since not all the multiple choice options have corresponding single options... But the multiple choice answers should be viewed with suspicion.

e, b, c, h, a, d, g, f.

Does choice (d) say psychotic or psychiatric?  I might go with that.

Is this really your top ten list that describes your favourite female Instructables member or members?


the UK perspective ;)


My answers, though inferring the type of person from these statements is not something that I would naturally do. Actions and presentation of the person to me is far more important than trying to draw vague conclusions from a short statement....
I always feel that these kinds of questions get more information from the person answering than they do about the person in the question (namely environment, past and their experiences), I just can't quite help it, but I keep thinking about the "interrogation scene" in BladeRunner. (hmmmm...tortoises...)

I believe that A and G are the two most likely, but to be sure, I would ask the CIA


8 years ago

I don't like the fact that some of the statements are orthogonal to each other.  C being true or false has no bearing on D being true or false.  H is also a conjunction of two ("job" and "feminist") so my inner statistician considers it less likely because it's more specific.

Numerical "probability" is a pain- just speaking in terms of odds you have a better chance of guessing the colour of her eyes than her job just because there is less choice.  Similarly, I would imagine you have a better chance of guessing feminist or not (2 options) than which job (hundreds of options, most not covered by the options).

The only one I would like to draw any kind of causal connection from the opening statement to is D, because intelligence, having a philosophical degree and being concerned with discrimination/social justice would tend to indicate an interest in that type of job over book sales, insurance etc.  (Adjust "probability" of this for relative numbers of bookshop workers, insurance salespeople and social workers as per previous paragraph.)  Most of the rest I consider to be plausible, not unlikely or very likely, and not greatly affected by the statement.

In other (fewer) words, I consider D to be the only one I consider much more likely having read the original statement.


My inner cynic, having shoved the inner statistician away, says this is trying to  investigate a patriarchal society's fear/hatred of strong female personalities, but then I have been reading Oliver James.

I'd have to think either A, C, or D.

 Having only been given a two line description, I would choose -

I) Any of the above