Are You a Cognitive Miser?

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A) Yes.

B) No.

C) Cannot be determined.

This is from this month’s Scientific American — article unfortunately costs money. It’s about “dysrationalia,” which is what happens when people with nominally high IQ’s end up thinking irrationally. A phenomenon I’m sure we’ve all encountered, especially in certain corners of the blogosphere.

And the answer is the first option. But over 80 percent of people choose the third option. Here’s the solution: the puzzle doesn’t say whether Anne is married or not, but she either is or she isn’t. If Anne is married, she’s looking at George, so the answer is “yes”; if she’s unmarried, Jack is looking at her, so the answer is still “yes.” The underlying reason why smart people get the wrong answer is (according to the article) that they simply don’t take the time to go carefully through all of the possibilities, instead taking the easiest inference. The patience required to go through all the possibilities doesn’t correlate very well with intelligence.

108 Comments

108 thoughts on “Are You a Cognitive Miser?”

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  2. I’m surprised that the programmers claim that their training in debugging protects them from this error. I have an emprical, even dialectical, approach to debugging: study the problem for awhile, several steps where I make a change or two and rerun the program to get a better idea of what is going on, study some more, try changing and rerunning the program some more, etc. Rarely do I just sit down and try to work out every case. Probably not patient enough.

  3. Some comments I put on Sean’s FB account – must remember the blog. I like the syntax suggestion too – ‘is not’ directs away from the married-unmarried binary.

    1) These cognitive deficits are highly context dependent. E.g.:

    Jack is looking at Pat but Pat is looking at Georgette. Jack’s male but Georgette is not. Is a male looking at a female?

    I bet a lot more people would get that right. Some categories are much easier to reason about.

    My example is supposed to show that you can’t analyse these deficincies simply in terms of the form of the problem. It’s not so much laziness as misidentifying the kind of problem – and not so much stupidity as having a ‘heuristic’ for some other important kind of problem hard wired. It takes effort and training to overcome the innate misidentification of the problem (again in part caused by the specific categories involved – marital status vs gender); hence the cognitive cost. I guess the heuristic was selected for at some stage – who knows, perhaps day to day it still gets enough right to be more useful than taking the time to think things through! Of course for big things it could be catastrophic but is there any evidence that this defect still applies in life or death situations rather than the unreaistic toy examples we been discussing?

    I came up with a suggestion about the problem riding in to work this morning, in between dodging trucks. That is, the way the question is posed suggests that it is a kinship problem, and so the natural thing to do is to try solving it with kinship heuristics (I think it’s more than reasonable to suppose we evolved to have those), which of course are useless here – again, the ‘cost’ is in finding another approach to the problem, not in sorting through the possibilities – something much higher. So, as you described it, the Sci Am article sounds pretty much wrong to me.

    Finally, a random speculation. Maybe some people are both smart and stereotypically impractical because these heuristics have less of a grip on their thought processes – because they suffer from a cognitive deficiency (relative to some problem scenarios)!

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  5. Based on, “The patience required to go through all the possibilities doesn’t correlate very well with intelligence.” Should i consider myself stupid since i said “Yes”?

  6. This example is a bad analogy to the majority of problems faced in the real world. In the real world, “Anne” is usually not in a yes or no state (2 options; married or unmarried), but is instead in one of many unknown states. From conditioning, our behavior has been molded to not try and figure out all of the possible states for “Anne” or a minor problem like this one since this is usually not possible and a waste our time. Making the possible false assumption that “Anne” is in one of two states (married or unmarried) will usually give you more false conclusions in the real world than the number of false conclusions that come from running into the above problem. Now if getting the wrong answer to this problem actually had a negative outcome on your life, then I am sure more people would have taken the time to work out all of the possibilities and get the correct answer.

  7. The analogous examples described in:
    #34, DP in CA
    #53, Nick

    show that a change of interpretation of the entities and the actions they do makes the problem much easier to get right quickly.

    It reminds me of another logic puzzle, which was difficult to figure out when the entities were labeled as “A”, “B” and “C”, but easy to sort out when they were described as “Alice”, “Bob” and “Carol”. (I don’t remember the specific details of the puzzle.) In that case, it seemed that the use of the names plugged into a mental module that we all seem to have for processing relationships: Probably a useful mental capability for operating within a social group!

    Whereas in the case of this puzzle, somehow the invocation of that module gives a misleading push to one’s direction of thought. Perhaps because there is NO social/behavioral connection between the status of being married and the action of looking at someone else.

    However, there IS an obvious tie-in between being male/female and the action of looking at someone else (also male/female). So in that case, the invocation of the mental module might help.

    In the case of the cards covering each other, there is no social aspect at all, so the mental module is not invoked at all: Hence, no confusion.

    The relation between these tests and “intelligence”? Well, the most common application of intelligence is dealing with other people, so it makes sense that intelligence is correlated with the activity of the mental module. In the instant case, this module is hurting performance on this test. So intelligence SHOULD be negatively correlated with this test.

    The people who did well on this test are either weak in the mental module (“dumber”), or else somewhat alienated from other people (“socially dumber”). I probably fit into the second sub-category.

  8. Someone using classical logic would of course derive the answer (A) to this question. However, I must note that someone using intuitionistic logic would get the answer (C). Intuitionistically, let A = “Anne is married”, and B = “a married person is looking at an unmarried person”. We know that A implies B (since then Ann is looking at George), and we also know that not-A implies B (since then Jack is looking at Ann) — but intuitionistically, we can’t derive B from these two statements. (If we could, we could derive excluded middle, which is not an intutionistic theorem.)

    Another way of thinking about this is that intuitionistic derivations should be “constructive” — we should be able to find an example of a married person looking at an unmarried person. But if we don’t know Ann’s marital status, we can’t come up with such an example.

  9. Alex R, yes, that’s also what I meant in my reply, but I didn’t want to use the logic jargon. Nobody should beat themselves up too much for missing an existence proof in this context; we don’t as much care about “there exists a married person” as “this particular married person”. I believe if the question was phrased differently (e.g. with live wires and bombs, etc.) I am guessing more people might get it right.

  10. Sheesh, I’m feeling stupid BECAUSE I got it right. -_- Should I feel that way cause I stoped to read again, or should I feel good because I stopped and read again? I’ve heard that IQ doesnt necesarily go hand in hand with intelligence, but still. Thats a depressing read.

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  12. Listen, Ann is divorced. She no longer believes in marriage and is likely to start playing for the other team. Jack is married and thinks she’s cute but all he can do is stare, since he is married. Annoyed, Ann looks at George who is a clueless middle-aged man who ponders trick questions for enjoyment.

  13. Wonderful discussion. Much better than the puzzle itself.
    The only additional point I would like to emphasize is that changing your way of thinking about such puzzles is what graduate school is all about today in the U.S.A. Critically thinking through medical data that may be contradictory, complimentory or neither is key to good medical decision making. (While avoiding those heuristics, which scare me silly!)
    Training IS the difference on whether or not this is answered correctly. Training is what gives you the tools to separate the social paradigm out from the problem as well as objectify the individuals Iyes, while isolating us and perhaps making us socially “dumber” it is a useful skill) and use a A,B, C schema instead of getting wrapped up in extraneous detail. I guess I am saying…while intelligence may not be correlated with patience, speed IS important when dealing with a roomful of Patients. So, intelligence or training, I still think it is a fair test.
    I guess I am just saying, respect those who have worked hard to develop these skills in order to serve you. It might just save your life…
    Yes, quite obviously, I got it right.

  14. I agree with those who say it’s not really about patience. I think it’s simply more efficient to skip the thinking and read the readily available answer.

    (No, I don’t really think that. Yeah, I got it wrong too. Dammit.)

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  16. I really thought Anne could be a donkey or a mannequin or something.

    If it would have said “The three of them are real people” then I would have probably thought a bit more.

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  18. I think the reasoning that most of us probably went through was something like this…

    We don’t know whether Anne is married. Therefore we don’t know (A) whether Jack is looking at an unmarried person, or (B) whether a married person is looking at George.

    So far that’s correct. But then we continue… Since we don’t know either A or B, we don’t know whether either of them is true.

    But that step is not logically valid. We can know (A OR B) without knowing either A or B. To put it another way, we can know that one of them is true without knowing which one.

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  20. I took the right answer but started to feel skeptical about it later on.

    Anyway, I think you can disagree about fundamental issues. Do you agree or disagree?

  21. Lol at @49 SFJP.

    Based on reactions I have to say the problem is designed to make everyone feel bad, if you picked C you got owned by a simple puzzle, if you picked A your intelligence is being questioned if you picked B not only you got it wrong your heuristics which the problem exploits to induce wrong answer is not working.

    Sean stop alienating your readers 😛 BTW which one did you pick?

  22. Yeah, I got it right but now I’m questioning my intelligence.

    Though a few points: it does say that 80% of people got it wrong, so it can’t be only above-average intelligence people answering incorrectly (unless, did they only give it to high intelligence people?)

    And also it doesn’t say patience is anti-correlated with intelligence, just not strongly correlated. Though it seems the more I believe myself to be “smart”, the more likely I am to make silly mistakes (my ego seems extremely detrimental to my intelligence.)

  23. It’s a philosophical question.

    Not all schools of mathematical philosophy (e.g. intuitionists as per Brouwer) accept the law of the excluded middle, i.e. that either A or not A.

    Actually, that is true, but I still don’t think it applies here, because we know that for being married or , the law of the excluded middle does apply.

  24. Pingback: Having patience is part of being smart « Later On

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