## LESSWRONGLW

My point was that I don't know where to assume the linearity is. Whenever I have private randomness, I have linearity over what I end up choosing with that randomness, but not linearity over what probability I choose. But I think this is non getting at the disagreement, so I pivot to:

In your model, what does it mean to prove that U is some linear affine function? If I prove that my probability p is 1/2 and that U=7.5, have I proven that U is the constant function 7.5? If there is only one value of p, it is not defined what the utility function is, unless I successfully carve the universe in such a way as to let me replace the action with various things and see what happens. (or, assuming linearity replace the probability with enough linearly independent things (in this case 2) to define the function.