You can read the first thread, the post for a short description of the theoretical reasons for giving up $100 (expected utility, reflective consistency), and more in the comments.
As I noted, I’m not sure it’s what you really should do, as a human, but it looks like it. I changed my mind about this conclusion a couple of times since the problem statement, first believing that you should give up $100, because it was what the UDT suggested, then that you shouldn’t, remembering that human brain probably does erase the counterfactual preference; now I’m back to being unsure about what goes on in the human brain, but trusting the normative theory as a better standard for decisions in the meantime.
Reading through the comments of that post, I understood this to be the gist of the argument for why you would give up the $100:
Before knowing the outcome of the coin flip, you would have taken the wager to pay $100 for a 50% chance to win $10000. Alternatively, if Omega had asked you to “precommit” $100 in case you lost, you would still agree—its nearly exactly the same thing. (Technically it’s an even better wager.) What if Omega asks you to precommit a witless future self? You would like to pre-commit your future self.
So you, your current self, while trying to decide whether to pay Omega or not, have decided that you would actually like to precommit a future self to paying the $100. How do you do that? By being that future person in the present and committing your current self to pay the $100. Indeed you lost, but being consistent with “being a payer” is what you decided you wanted.
You can read the first thread, the post for a short description of the theoretical reasons for giving up $100 (expected utility, reflective consistency), and more in the comments.
As I noted, I’m not sure it’s what you really should do, as a human, but it looks like it. I changed my mind about this conclusion a couple of times since the problem statement, first believing that you should give up $100, because it was what the UDT suggested, then that you shouldn’t, remembering that human brain probably does erase the counterfactual preference; now I’m back to being unsure about what goes on in the human brain, but trusting the normative theory as a better standard for decisions in the meantime.
Reading through the comments of that post, I understood this to be the gist of the argument for why you would give up the $100:
Before knowing the outcome of the coin flip, you would have taken the wager to pay $100 for a 50% chance to win $10000. Alternatively, if Omega had asked you to “precommit” $100 in case you lost, you would still agree—its nearly exactly the same thing. (Technically it’s an even better wager.) What if Omega asks you to precommit a witless future self? You would like to pre-commit your future self.
So you, your current self, while trying to decide whether to pay Omega or not, have decided that you would actually like to precommit a future self to paying the $100. How do you do that? By being that future person in the present and committing your current self to pay the $100. Indeed you lost, but being consistent with “being a payer” is what you decided you wanted.