How much would you pay to see a typical movie? How much would you pay to see it 100 times?

How much would you pay to save a random stranger’s life? How much would you pay to save 100 strangers?

If you are like a typical human being, your answers to both sets of questions probably exhibit failures to aggregate value linearly. In the first case, we call it boredom. In the second case, we call it scope insensitivity.

Eliezer has argued on separate occasions that one should be regarded as an obvious error to be corrected, and the other is a gift bestowed by evolution, to be treasured and safeguarded. Here, I propose to consider them side by side, and see what we can learn by doing that.

(Eliezer sometimes treats scope insensitivity as a simple arithmetical error that the brain commits, like in this quote: “the brain can't successfully multiply by eight and get a larger quantity than it started with”. Considering that the brain has little trouble multiplying by eight in other contexts and the fact that scope insensitivity starts with numbers as low as 2, it seems more likely that it’s not an error but an adaptation, just like boredom.)

The nonlinearities in boredom and scope insensitivity both occur at two different levels. On the affective or hedonic level, our emotions fail to respond in a linear fashion to the relevant input. Watching a movie twice doesn’t give us twice the pleasure of watching it once, nor does saving two lives feel twice as good as saving one life. And on the level of decision making and revealed preferences, we fail to act as if our utilities scale linearly with the number of times we watch a movie, or the number of lives we save.

Note that these two types of nonlinearities are logically distinct, and it seems quite possible to have one without the other. The refrain “shut up and multiply” is an illustration of this. It exhorts (or reminds) us to value lives directly and linearly in our utility functions and decisions, instead of only valuing the sublinear emotions we get from saving lives.

We sometimes feel bad that we aren’t sufficiently empathetic. Similarly, we feel bad about some of our boredoms. For example, consider a music lover who regrets no longer being as deeply affected by his favorite piece of music as when he first heard it, or a wife who wishes she was still as deeply in love w...

Scope Insensitivity

See also