Yes, indeed quite important. This is a common confusion that has often lead me down weird conversational paths. I think some microeconomics has most made this clear to me, because in there you seem to be constantly throwing tons of affine transformations at your utility functions to make them convenient and get you analytic solutions, and it becomes clear very quickly that you are not preserving the relative magnitude of your original utility function.
I think one of the reasons it took me so long to notice was that I was introduced to VNM utility I’m the context of game theory, and winning at card games. Most of those problems do have the property of the utility of some base scoring system composing well to generate the utility of various end games. Since that was always the case, I guess I thought that it was a property of utility, and not the games.
Yes, indeed quite important. This is a common confusion that has often lead me down weird conversational paths. I think some microeconomics has most made this clear to me, because in there you seem to be constantly throwing tons of affine transformations at your utility functions to make them convenient and get you analytic solutions, and it becomes clear very quickly that you are not preserving the relative magnitude of your original utility function.
I think one of the reasons it took me so long to notice was that I was introduced to VNM utility I’m the context of game theory, and winning at card games. Most of those problems do have the property of the utility of some base scoring system composing well to generate the utility of various end games. Since that was always the case, I guess I thought that it was a property of utility, and not the games.