GuySrinivasan comments on Quick puzzle about utility functions under affine transformations

• What they said about the U(-)=0 prob­lem. But the way I think about it re­solves more con­tra­dic­tions, more eas­ily, IMO.

• Utility is no more than a math­e­mat­i­cal ar­ti­fact, do not phrase ques­tions in terms of utility

Utility func­tions are equiv­a­lent un­der pos­i­tive af­fine trans­forms. This is a huge clue that think­ing about util­ity will lead to ma­jor in­tu­ition prob­lems. In­stead, use quan­tities that are not am­bigu­ous. You’re gonna have to get rid of the a and b in au(x)+b, so you’re go­ing to need three states of the world, always, be­fore you’re al­lowed to use in­tu­ition. You can com­bine them in differ­ent ways, but I like

r = [U(x)-U(z)] /​ [U(y)-U(z)]

Mere differ­ences in util­ity are not pinned down, be­cause of scale. Ra­tios of differ­ences in util­ity are great, though. It’s 2.67x as good to go from noth­ing to choco­late as to go from noth­ing to vanilla. 0 and 3 and 8, or 4 and 7 and 12, those are just there for com­pu­ta­tional con­ve­nience in some cir­cum­stances and can be ig­nored.