I'm partial to the surreals myself. Every ordered field is a subfield of the surreals, though this is slightly cheating since the elements of a field form a set by definition but there are also Fields, which have elements forming a proper class. The surreals themselves are usually a Field, depending on your preference of uselessly abstract set theory axioms. We know that we want utilities to form an ordered field (or maybe a Field?), but Dedekind completeness for utilities seems to violate our intuitions about infinite ethics.
I haven't studied the hyperreals, though. Is there any reason that you think they might be useful (the transfer principle?) or do you just find them cool as a mathematical structure?
I haven't studied the hyperreals, though. Is there any reason that you think they might be useful (the transfer principle?) or do you just find them cool as a mathematical structure?
They allow us to extend real-valued utilities, getting tractable "infinities" in at least some cases.
A few weeks ago at a Seattle LW meetup, we were discussing the Sleeping Beauty problem and the Doomsday argument. We talked about how framing Sleeping Beauty problem as a decision problem basically solves it and then got the idea of using same heuristic on the Doomsday problem. I think you would need to specify more about the Doomsday setup than is usually done to do this.
We didn't spend a lot of time on it, but it got me thinking: Are there papers on trying to gain insight into the Doomsday problem and other anthropic reasoning problems by framing them as decision problems? I'm surprised I haven't seen this approach talked about here before. The idea seems relatively simple, so perhaps there is some major problem that I'm not seeing.