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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.”

Relat­ed read­ing and teasers:

- Why Smart Brains Make Stu­pid Deci­sions

- 50 brain teasers to test your cog­ni­tive abil­i­ty.

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18 Responses

  1. Devin says:

    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.

  2. Rangoli says:

    I agree with Devin.

  3. Malfist says:

    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?

  4. Devin says:

    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?

  5. David Osborne says:

    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?

  6. Alvaro says:

    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 🙂

  7. sumanth says:

    Davis:
    well, your log­ic would be apt if sec­ond choice was ‘banker’ OR ‘fem­i­nist’ than ‘banker’ AND ‘fem­i­nist’. 🙂

  8. Devin says:

    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/

  9. Non says:

    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?

  10. Paul Dundon says:

    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.

  11. Alvaro says:

    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.

  12. Andy Manjuck says:

    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.

  13. 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.

  14. dwindle says:

    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.

  15. Alvaro says:

    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?

  16. Flo says:

    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.

  17. PJ says:

    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

  18. Cassady says:

    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!

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