Tuesday 25 January 2022

Good Guesses

This post is by Kevin Dorst and Matthew Mandelkern whose paper, "Good Guesses", is forthcoming in Philosophy and Phenomenological Research. The authors have written another post on guessing and the conjunction fallacy which you can read here.

Matthew Mandelkern

Where do you think Latif will go to law school? He’s been accepted to Yale, Harvard, Stanford, and NYU. We don’t know his preferences, but here’s the proportion of applicants with the same choices who’ve gone to each:

Yale, 38%; Harvard, 30%; Stanford, 20%; NYU, 12%.

So take a guess: Where do you think he’ll go?

Some observations: One natural guess is ‘Yale’. Another is ‘Either Yale or Harvard’; meanwhile, it’s decidedly unnatural to guess ‘not Yale’, or ‘Yale, Stanford, or NYU’.

Though robust, these judgments are puzzling. ‘Yale’ is a fine guess, but its probability is below 50%, meaning that its negation is strictly more probable (38% vs. 62%); nevertheless, ‘not Yale’ is a weird guess. Moreover, ‘Yale or Harvard’ is a fine guess—meaning that it’s okay to guess something other than the single most likely school—yet ‘Yale, Stanford, or NYU’ is a weird guess (why leave out ‘Harvard’?). This is so despite the fact that ‘Yale or Harvard’ is less probable than ‘Yale, Stanford, or NYU’ (68% vs. 70%).

Kevin Dorst

In this paper we generalize these patterns (following HolguĂ­n 2020) and develop an account that explains them. The idea is that guessers aim to optimize a tradeoff between accuracy and informativity—between saying something that’s likely to be true, and saying something that’s specific.

As William James (1897) famously pointed out, these goals directly compete: the more informative an answer is, the less probable it will be. Some people will put more weight on informativity, guessing something specific like ‘Yale’. Others will put more weight on accuracy, guessing something probable like ‘Yale, Harvard, or Stanford’.

 Neither of these guesses are mistakes; they’re just different ways of weighing accuracy against informativity. But on the way we spell this out, every permissible way of making this tradeoff will lead ‘not Yale’ and ‘Yale, Stanford, or NYU’ to be bad guesses. Why? In each case, there is an equally-informative but more probable answer: ‘Not NYU’ and ‘Yale, Harvard, or Stanford’, respectively.

Now consider a different question.

Linda is 31 years old, single, and very bright. As an undergraduate she majored in philosophy and was highly active in social-justice movements. Which of the following do you think is more likely?

1) Linda is a bank teller.

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

Famously, Tversky and Kahneman (1983) found that most people choose (2) over (1). However, every way of (2) being true is a way of (1) being true, therefore it can’t be more likely! This is known as the conjunction fallacy: ranking a specific claim as more probable than a broader claim.

But notice: by the exact same token, every way in which ‘Yale’ would be a true guess is also a way in which ‘Yale, Stanford, or NYU’ would be true. Yet—for the reasons mentioned above—the former is a good guess, the latter is a weird one: sometimes a drive for informativity can make it reasonable to give an answer that’s less probable than some of the alternatives. Thus, perhaps, a preference to choose the conjunction (2) can be explained by the fact that it’s more informative than (1).

In this paper, we argue that this is so. We make the case that much of our reasoning under uncertainty involves negotiating an accuracy-informativity tradeoff, and that this helps to explain a variety of patterns in the things people tend to guess, believe, and assert.  

We then bring this tradeoff to bear on the conjunction fallacy. We argue that it helps to explain—and partially rationalize—a variety of subtle empirical effects that have been found in people’s tendency to commit this fallacy.

Upshot: maybe we weren’t dumb for thinking (guessing) that Linda is a feminist bank teller, after all. 


  1. An alternative explanation of the Linda case is that people hear "Linda is a bank teller" as "Linda is a bank teller who is not active in the feminist movement" when juxtaposed with "Linda is a bank teller and is active in the feminist movement".

  2. Isn't much of this due to what is being implied by the questions? In the bank teller case, in the context of being offered both choices, I'd be likely to read 1)as "a bank teller and not a feminist." Similarly, I don't see the law school question as asking me to say the most accurate thing (which would be "a law school" - accurate but uninformative) but as asking me to pick a particular school, so I'd guess Yale.

  3. This is super interesting! Here is a quick question. You seem to assume that, for example, my "Yale or Harvard" answer is an expression of my commitment to disjunction "Either Latif will go to Yale or Harvard". Alternatively, one might think that my "Yale or Harvard" answer is rather an expression of something like; "Yale" and "Harvard" are beyond my threshold (say 25%), and others are not.

    Similarly, "not Yale" expresses something like; even "Yale" is not beyond my threshold (say 50%). Its weirdness is perhaps due to the fact that threshold is too high in this particular context. Again "Yale, Stanford, or NYU" expresses something like ; "Yale", "Stanford" and "NYU" are beyond my threshold. Its weirdness is perhaps due to the fact that if "Stanford" and "NYU" is beyond the threshold, then "Harvard" is beyond it too; but "Harvard" is not mentioned, which is puzzling.


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