It does occur to me that while giving the people an order migth be suspicous utilities are a shorthand of preferences which are defined to be orders of preferring a over b. Therefore there is anyways going to be a conversion to ordinals so surreals should remain relevant.
I don’t think I’m convinced. Firstly, because in these cases where we’re looking at aggregating the interests of large collections of people it’s the people, not the possibilities, that seem like they need to be treated as ordered. Secondly, because having an ordering on preferences isn’t at all the same thing as wanting to use anything like ordinals for them. (E.g., cardinals are ordered too—well-ordered, even—at least if we assume the axiom of choice. The real numbers are ordered in the obvious way, but that’s not a well-ordering. Etc.)
I concede that what I’m saying is very hand-wavy. Maybe there really is a good way to make this sort of thing work well using surreal numbers as utilities. And (perhaps like you) I’ve thought for a long time that using something like the surreals for utilities might turn out to have advantages. I just don’t currently see an actual way to do it in this case.
It does occur to me that while giving the people an order migth be suspicous utilities are a shorthand of preferences which are defined to be orders of preferring a over b. Therefore there is anyways going to be a conversion to ordinals so surreals should remain relevant.
I don’t think I’m convinced. Firstly, because in these cases where we’re looking at aggregating the interests of large collections of people it’s the people, not the possibilities, that seem like they need to be treated as ordered. Secondly, because having an ordering on preferences isn’t at all the same thing as wanting to use anything like ordinals for them. (E.g., cardinals are ordered too—well-ordered, even—at least if we assume the axiom of choice. The real numbers are ordered in the obvious way, but that’s not a well-ordering. Etc.)
I concede that what I’m saying is very hand-wavy. Maybe there really is a good way to make this sort of thing work well using surreal numbers as utilities. And (perhaps like you) I’ve thought for a long time that using something like the surreals for utilities might turn out to have advantages. I just don’t currently see an actual way to do it in this case.