David Gordon Misconstrues the Linda Problem

Kahneman and Tversky famously posited that there is a "conjunction fallacy": people often assign a higher probability to a "plausible" case with more specific conditions than a general one. That clearly is erroneous.

David Gordon tries to deny Kahneman and Tversky have exposed any error in people's reasoning. He writes:

"I do not think this result demonstrates that the people in the survey have reasoned wrongly. Suppose, when asked about the probability of Linda's occupation, people think it very unlikely that she has chosen to be a bank teller. They think, by contrast, that she very likely identifies with feminism. When asked about Linda's being both a feminist and bank teller, they may not recall their earlier estimate of her being a teller. Rather, they may simply lower their estimate that she is a feminist, to reflect the new information that she is also a teller."

The reason Gordon tries to debunk Kahneman and Tversky is clear: as a market fundamentalist, he cannot bear any suggestion that market actors are not perfectly rational. But his response is ludicrous: first of all, the experimental subjects were not given "new information that [Linda] is also a teller": they were asked to assign probabilities to various statements about her. Never were they told that one of the statements is true!

But even worse, Gordon's "they may not recall" is far, far worse for the hypothesis that market actors behave rationally than is Kahneman and Tversky's interpretation of their result. Kahneman and Tversky actually gave subjects these two statements in immediate succession:

1) Linda is a bank teller.
2) Linda is a bank teller and is active in the feminist movement.

Gordon is claiming that there is no failure of rationality here, because, five or ten seconds after assigning a probability to statement 1, the subjects have no memory of what they just did, and assign a probability to statement 2 from a blank slate.

If people's short-term memories are really that bad, it is hard to see why workers hired by a company at time T can even remember who they work for at time T + 5 seconds! Farmers who have picked apples at time T will not even remember they have any apples at time T + 5 seconds! It is very hard to see how markets can work under such conditions.

The right way for libertarians to respond to these findings, I think, is to note that government actors have the same biases as market actors, not to deny the findings of scientific psychology!


  1. Anonymous9:38 PM

    "That clearly is erroneous"

    You might want to write that differently, because to me it sounds like you're contesting the fallacy. Of course, I know that you're doing the exact opposite. Indeed, the "Linda problem" is a case of faulty reasoning.

    David is a very smart guy that I admire, but it surprises me that he would take this tack. The reasoning is faulty because the probability of the two choices can be proved such that we can clearly see that the reasoning is faulty. That doesn't discount that Linda could indeed be both a bankteller and a feminist, only that it is faulty reasoning to think so based upon the given information and the probability of the choices conforming to our interpretation of that information (it would be less likely that she would be two things than just the one). And yeah, the memory thing was a stretch.

    I do take some offense (by association) to your "market fundementalist/perfectly rational" remark, though. And I don't think that it is the explanation for David's error (at least not in the way that you think).

    You know as well as I do that when speaking of rational actors, that this only pertains to the individual in a single instance of time: Everything that I do is rational to me, based upon my own logic.

    Of course, there is a dominant logic (generally correct reasoning) that can reveal to us what is correct reasoning vs incorrect reasoning, but I don't think that we all necessarily conform to this at all times and in all cases. Certainly, most people aren't aware of the conjunction fallacy, which explains why so many people commit it, but *they* thought that it was a perfectly rational choice at the time to choose number 2.

    As for your closing remark regarding libertarians, I fully agree! However, I don't think the bias presented in this context would elaborate on anything significant between government and market, at least not on its own.

  2. Another response (for defense of the market) is that actors in the market (be they persons, committees, or algorithms) either learn to overcome these biases or are driven out. Markets enforce and reward rationality at the expense of irrationality.

  3. Dr. Callahan,

    In the penultimate paragraph of his review, Gordon does note that state actors would be subject to the same irrationality as market actors;

    Even if one did have a philosophy that justified considerable state action, a further problem would arise — one that Ubel also ignores. Why should we think that existing states would act rationally to carry out the dictates of that philosophy? Would not holders of state power be subject to exactly the errors of rationality that Ubel complains about in participants in the free market?

    I also don't think he is denying that people act irrationally because he is challenging some of the findings of scientific psychologists. In the paragraph before his critique of the “conjunction fallacy” he writes this;

    How does it do so? For one thing, our heroes say, people often make mistakes in reasoning. If people reason wrongly, how can they hope to get what they really want? The fact that the market gives them what they choose has little significance if this choice results from logical failings. I do not deny the problem: far be it from me to claim that people reason infallibly. But a number of the examples that they cite to make their case strike me as unconvincing.

    And, following his critique he suggests an alternative set of (I think) reasonable questions, that, depending on how they were answered, would convince him that people do frequently engage in a “conjunctive fallacy.”

    He may be guilty of making a silly critique, but Gordon explicitly says people do make errors in reasoning, and that he would be convinced of more of the author’s findings had their research yielded certain answers to more carefully worded questions. I don’t think he is guilty of denying evidence of irrationality simply to protect his ‘market fundamentalist’ viewpoint.

  4. Thank you for your comments on my article. As I saw them only a short time ago, I hope you will allow me this late response. You have rightly caught my slip about “new information”; I ought to have said, “when someone is trying to estimate the probability that Linda is both a feminist and a librarian.” Certainly it would be “ludicrous" had I assumed a total failing of short-term memory. But I did not do so. I only suggested that a chooser might estimate the probability of Linda’s being a librarian differently when this was conjoined with her being a feminist from his estimate of that probability when asked to consider by itself her being a librarian. If someone did this, the fact that he had earlier differently estimated the probability of her being a librarian might not be salient to him. Whether there is anything to my suggestion is another matter—I don’t set much store by it---but the lapse I suggested was very far from a total memory collapse.
    Further, I do not deny that people make mistakes in practical reasoning: I am sure they often do so. I do think that a number of the arguments advanced in the book I reviewed to demonstrate these mistakes are flawed, but that is another matter. You think that I wish to ignore lapses of reasoning because I am a market fundamentalist who, anxious to block a case for state intervention, argues that people reason without error; but I have no such agenda. Eric Voegelin forty years ago warned me of the mistake of criticizing a writer by trying to assign him to a pre-conceived ‘”position”.


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