What you “did” there is full of type errors and treating the scales and offsets as significant and whatnot. That is not allowed, and you seemed to be claiming that it is not allowed.
Hm. You definitely did communicate that, but I guess maybe I’m pointing out a math mistake—it seems to me that you called the problem of arbitrary offsets solved too early. Though in your example it wasn’t a problem because you only had two outcomes and one outcome was always the zero point.
As I realized later because of Alex, the upshot is that to really deal with the problem of offsets you have to (at least de facto) normalize the relative utilities, not the utilities themselves. (On pain of stupidity)
Though in your example it wasn’t a problem because you only had two outcomes and one outcome was always the zero point.
I think my procedure does not run into trouble even with three options and other offsets. I don’t feel like trying it just now, but if you want to demonstrate how it goes wrong, please do.
the upshot is that to really deal with the problem of offsets you have to (at least de facto) normalize the relative utilities, not the utilities themselves. (On pain of stupidity)
Hm. You definitely did communicate that, but I guess maybe I’m pointing out a math mistake—it seems to me that you called the problem of arbitrary offsets solved too early. Though in your example it wasn’t a problem because you only had two outcomes and one outcome was always the zero point.
As I realized later because of Alex, the upshot is that to really deal with the problem of offsets you have to (at least de facto) normalize the relative utilities, not the utilities themselves. (On pain of stupidity)
I think my procedure does not run into trouble even with three options and other offsets. I don’t feel like trying it just now, but if you want to demonstrate how it goes wrong, please do.
I don’t understand what you are saying here.