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.
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%).
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.