Yeah. Here I’m trying to actually justify the existence of a numbering scheme that has the property that “increase of five points of utility is increase of five points of utility (in some set of utility units)”, no matter what the state that you’re starting and increasing from is.
I need to do this so that I then have a currency I can use in a dutch book style argument to build up the rest of it.
As far as Lexicographic preferences, I had to look that up. Thanks, that’s interesting. Maybe doable with hyperreals or such?
As far as risk aversion, um… unless I misunderstand your meaning, that should be easily doable. Simply have really increasingly huge steps of disutiliy as one goes down the preference chain, so even slight possibility of a low rank outcome would be extremely unpreferred?
I’m afraid all of this is all still a bit vague for me, sorry.
Are you familiar with the standard preference representation results in economics (e.g. the sort you’d find in a decent graduate level textbook)? The reason I ask is that the inability to represent lexicographic preferences is pretty well-known, and the fact that you weren’t aware of it makes me suspect even more strongly than before that you may be trying to do something that’s already been done to death without realizing it.
I think we’re talking past each other on the risk aversion front. Probably my fault, as my comment was somewhat vague. (Maybe also an issue of inferential distance.)
More I think about it though, seems like hyperreals, now that I know of them, would let one do a utility function for lexicographic preferences, no?
And nothing for you to apologize for. I mean, if there’s this much confusion about what I’m writing, it seems likely that the problem is at my end. (And I fully admit, there’s much basic material I’m unfamiliar with)
Yeah. Here I’m trying to actually justify the existence of a numbering scheme that has the property that “increase of five points of utility is increase of five points of utility (in some set of utility units)”, no matter what the state that you’re starting and increasing from is.
I need to do this so that I then have a currency I can use in a dutch book style argument to build up the rest of it.
As far as Lexicographic preferences, I had to look that up. Thanks, that’s interesting. Maybe doable with hyperreals or such?
As far as risk aversion, um… unless I misunderstand your meaning, that should be easily doable. Simply have really increasingly huge steps of disutiliy as one goes down the preference chain, so even slight possibility of a low rank outcome would be extremely unpreferred?
I’m afraid all of this is all still a bit vague for me, sorry.
Are you familiar with the standard preference representation results in economics (e.g. the sort you’d find in a decent graduate level textbook)? The reason I ask is that the inability to represent lexicographic preferences is pretty well-known, and the fact that you weren’t aware of it makes me suspect even more strongly than before that you may be trying to do something that’s already been done to death without realizing it.
I think we’re talking past each other on the risk aversion front. Probably my fault, as my comment was somewhat vague. (Maybe also an issue of inferential distance.)
More I think about it though, seems like hyperreals, now that I know of them, would let one do a utility function for lexicographic preferences, no?
And nothing for you to apologize for. I mean, if there’s this much confusion about what I’m writing, it seems likely that the problem is at my end. (And I fully admit, there’s much basic material I’m unfamiliar with)