Conjunction fallacy II

And a follow-up on the follow-up. Here is an idea for how to quantify the conjunction fallacy experimentally. Present the subjects with the standard “Linda” story:

Linda is thirty-one 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 antinuclear demonstrations.

But now, instead of asking them to choose the more probable outcome from the two standard options, (1) Linda is a bank teller (2) Linda is a bank teller and is active in the feminist movement, why not ask them to select from a longer list:

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.
  3. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college.
  4. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college and owns cats.
  5. Linda is a bank teller and is active in the feminist movement and had a lesbian experience in college and owns cats and is overweight.

What is the conjunction size at which the subject begins to realize that increasing the specificity of the outcome is making it less likely?

 

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6 thoughts on “Conjunction fallacy II

  1. What are you trying to measure, the imprecision of language? Get a book of quotations for that.

    I don’t think there’s a widespread “conjunction fallacy:” if your choices are (A) Linda is a bank teller and may or may not be a feminist or (B) Linda is a bank teller and definitely a feminist, you’d get somewhere near 100% answering A. (If not, then that’s actually newsworthy.)

    What might be a real thing is a “correlation fallacy.” Construct some question where the choices are Pr[A,B] more, less, or equal to Pr[A] Pr[B] when the story details give no indication. But even then, people’s priors come into play: if all the women’s college graduates in Philosophy you know are lesbians (my wife notwithstanding), then it’s hardly _irrational_ to use that information in your choice.

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  2. The point of my proposed experiment was to see how long it takes before the subject catches on. We know from experiments that when presented just 1 and 2, many people rank 2 as more probable. What about {1,2,3}, and so on?

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  3. This “layering” argument doesn’t validate Kahnemann/Twersky, since many people will interpret the options so as to be mutually exclusive (as this makes the Q & A most efficient and informative). If the progression goes

    1. bank teller,
    2. bank teller and Hillary Clinton voter in 2016 election,
    3. bank teller and Clinton voter and lesbian cat lady

    the winner will be 2 understood as ( bank teller + Clintonite + not a lesbian-cat-lady) since catlady (3) and Trump voter (1) are both relatively rare conditional on the given information.

    i.e. option number N is taken to mean “member at level N but no higher level of the progression”, and the respondent then considers probability distributions on a 3-element set.

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  4. I think there is a fully general psychological hypothesis here, which is that people are statistical (not logical) inference engines. When provided with more and more data on Linda that all correlate with degree of feminism, people start to estimate her position on their personal intuitive scale of feminism, and they most naturally think of and share with others the output of their thinking in the form of an estimate of her position (or confidence interval, Bayesian-like hyperdistribution, etc, stated in less formal terms) on that scale. It’s “lazy evaluation”, so they don’t make precise what they think until presented with the list of options, and the result becomes dependent on the list, but fundamentally they are trying to share the estimate. So Kahnemann’s question is naturally interpreted as a literal request for Maximum Likelihood decision between a list of mutually exclusive options; to interpret it otherwise people have to leave the cognitive framework they use constantly and successfully, and re-situate the question in the artificially learned setting of propositional/sentential logic.

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    1. Yes, I find this plausible. As I said in an earlier post, if you ask the average person “What’s the opposite of ‘always’?” they’ll blurt out “Never!”, which is logically the wrong answer (when interpreting ‘the opposite’ as logical negation).

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