I was discussing UDT yesterday and the question came up of how to treat uncertainty over your utility function. I suggested that this could be transformed into a question of uncertainty over outcomes. The intuition is that if you were to discover that apples were twice as valuable, you could simply pretend that you instead received twice as many apples. Is this approach correct? In particular, is it transformation compatible with UDT-style reasoning?

# 2 Answers

### Mar 18, 2019 link

19Utility functions are invariant up to affine transformation. I don't need to say how much I value a human life or how much I value a chicken life to make decisions in weird trolly problems involving humans and chickens. I only need to know relative values. However, utility uncertainty messes this up. Say I have two hypotheses: one in which human and chicken lives have the same value, and one in which humans are a million times more valuable. I assign the two hypotheses equal weight.

I could normalize and say that in both cases a human is worth 1 util. Then, when I average across utility functions, humans are about twice as valuable as chickens. But if I normalize and say that in both cases a chicken is worth 1 util, then when I average, the human is worth about 500,000 times as much. (You can still treat it like other uncertainty, but you have to make this normalization choice.)

if you were to discover that apples were twice as valuable, you could simply pretend that you instead received twice as many apples

No, because twice as many apples are not usually twice as valuable. This because utility functions are not linear.

You can kind of deal with uncertainty about utility by fudging expectations about outcomes but, trust me, it is the primrose path to hell.