The 12-billion-utils example is similar to one I mention on this page under “What about Isolated Actions?” I agree that our decision here is ultimately arbitrary and up to us. But I also agree with the comments by others that this choice can be built into the standard expected-utility framework by changing the utilities. That is, unless your complaint is, as Nick suggests, with the independence axiom’s constraint on rational preference orderings in and of itself (for instance, if you agreed—as I don’t—that the popular choices in the Allais paradox should count as “rational”).
No, I don’t agree that the Allais paradox should count as rational—but I don’t need to use the independence axiom to get to this. I’ll re-explain in a subsequent post.
The 12-billion-utils example is similar to one I mention on this page under “What about Isolated Actions?” I agree that our decision here is ultimately arbitrary and up to us. But I also agree with the comments by others that this choice can be built into the standard expected-utility framework by changing the utilities. That is, unless your complaint is, as Nick suggests, with the independence axiom’s constraint on rational preference orderings in and of itself (for instance, if you agreed—as I don’t—that the popular choices in the Allais paradox should count as “rational”).
No, I don’t agree that the Allais paradox should count as rational—but I don’t need to use the independence axiom to get to this. I’ll re-explain in a subsequent post.