Scope Insensitivity - Explanation and examples

How does our intuition process large numbers? It doesn't.


What is scope insensitivity?

I'm not very good at feeling the size of large numbers. Once you start tossing around numbers larger than 1000 (or maybe even 100), the numbers just seem "big".
Consider Sirius, the brightest star in the night sky. If you told me that Sirius is as big as a million earths, I would feel like that's a lot of Earths. If, instead, you told me that you could fit a billion Earths inside Sirius… I would still just feel like that's a lot of Earths.
The feelings are almost identical. In context, my brain grudgingly admits that a billion is a lot larger than a million, and puts forth a token effort to feel like a billion-Earth-sized star is bigger than a million-Earth-sized star. But out of context — if I wasn't anchored at "a million" when I heard "a billion" — both these numbers just feel vaguely large.

On Caring, Nate Soares

The key insight to scope insensitivity is that our System 1 (intuition/gut feeling) is bad at dealing with numbers, and we shouldn’t trust it. It was developed for an environment very foreign to what we currently face. I might not feel a large emotional difference between helping my friend with their homework, or creating a product that helps everyone with their homework, but if it takes me the same amount of time, I should clearly do the latter if it actually helps more people.

Examples of scope insensitivity

In one study, respondents were asked how much they were willing to pay to prevent migrating birds from drowning in uncovered oil ponds by covering the oil ponds with protective nets. Subjects were told that either 2,000, or 20,000, or 200,000 migrating birds were affected annually, for which subjects reported they were willing to pay $80, $78 and $88 respectively. In the first case, we value saving a bird at 4 cents per bird, but in the last case, at 0.00044 cents. If a bird not suffering is worth some amount, it shouldn’t change when we have the opportunity to help another bird.

Also check out

  1. Shut up and multiply, LessWrong
  2. Scope neglect, Wikipedia

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