“The problem with your solution is that it’s not complete in the formal sense: you can only say some things are better than other things if they strictly dominate them, but if neither strictly dominates the other you can’t say anything.”
As I said earlier, my solution is an argument that in every case there will be an action that strictly dominates all the others. (Or, weaker: that within the set of all hypotheses of probability less than some finite N, one action will strictly dominate all the others, and that this action will be the same action that is optimal in the most probable hypothesis.) I don’t know if my argument is sound yet, but if it is, it avoids your objection, no?
I’d love to understand what you said about re-arranging terms, but I don’t. Can you explain in more detail how you get from the first set of hypotheses/choices (which I understand) to the second?
I’d love to understand what you said about re-arranging terms, but I don’t. Can you explain in more detail how you get from the first set of hypotheses/choices (which I understand) to the second?
I just moved the right hand side down by two spaces. The sum still stays the same, but the relative inequality flips.
As I said earlier, my solution is an argument that in every case there will be an action that strictly dominates all the others.
Why would you think that? I don’t really see where you argued for that, could you point me at the part of your comments that said that?
OH ok I get it now: “But clearly re-arranging terms doesn’t change the expected utility, since that’s just the sum of all terms.” That’s what I guess I have to deny. Or rather, I accept that (I agree that EU = infinity for both A and B) but I think that since A is better than B in every possible world, it’s better than B simpliciter.
The reshuffling example you give is an example where A is not better than B in every possible world. That’s the sort of example that I claim is not realistic, i.e. not the actual situation we find ourselves in. Why? Well, that was what I tried to argue in the OP—that in the actual situation we find ourselves in, the action A that is best in the simplest hypothesis is also better.… well, oops, I guess it’s not better in every possible world, but it’s better in every possible finite set of possible worlds such that the set contains all the worlds simpler than its simplest member.
I’m guessing this won’t be too helpful to you since, obviously, you already read the OP. But in that case I’m not sure what else to say. Let me know if you are still interested and I”ll try to rephrase things.
Sorry for taking so long to get back to you; I check this forum infrequently.
Again, thanks for this.
“The problem with your solution is that it’s not complete in the formal sense: you can only say some things are better than other things if they strictly dominate them, but if neither strictly dominates the other you can’t say anything.”
As I said earlier, my solution is an argument that in every case there will be an action that strictly dominates all the others. (Or, weaker: that within the set of all hypotheses of probability less than some finite N, one action will strictly dominate all the others, and that this action will be the same action that is optimal in the most probable hypothesis.) I don’t know if my argument is sound yet, but if it is, it avoids your objection, no?
I’d love to understand what you said about re-arranging terms, but I don’t. Can you explain in more detail how you get from the first set of hypotheses/choices (which I understand) to the second?
I just moved the right hand side down by two spaces. The sum still stays the same, but the relative inequality flips.
Why would you think that? I don’t really see where you argued for that, could you point me at the part of your comments that said that?
OH ok I get it now: “But clearly re-arranging terms doesn’t change the expected utility, since that’s just the sum of all terms.” That’s what I guess I have to deny. Or rather, I accept that (I agree that EU = infinity for both A and B) but I think that since A is better than B in every possible world, it’s better than B simpliciter.
The reshuffling example you give is an example where A is not better than B in every possible world. That’s the sort of example that I claim is not realistic, i.e. not the actual situation we find ourselves in. Why? Well, that was what I tried to argue in the OP—that in the actual situation we find ourselves in, the action A that is best in the simplest hypothesis is also better.… well, oops, I guess it’s not better in every possible world, but it’s better in every possible finite set of possible worlds such that the set contains all the worlds simpler than its simplest member.
I’m guessing this won’t be too helpful to you since, obviously, you already read the OP. But in that case I’m not sure what else to say. Let me know if you are still interested and I”ll try to rephrase things.
Sorry for taking so long to get back to you; I check this forum infrequently.