My state of knowledge pre-coin toss does not include knowledge of what the coin is. However, with all the caveats, omniscience and counterfactuals thrown in, the state of knowledge that I have when I actually make the decision is that there is a 2⁄2 chance of the coin being tails. Omnisicence + hypercommunication to a decision based on the known outcome effectively gives full disclosure.
I retract this statement. I have a suspicion that the addition of the ‘least convenient world’ criterion has overwhelmed my working memory with my current expertise in exotic decision making. I would need to think more on exactly what the implications are of novel restrictions before I could be confident.
I will say that in the situation you describe I would give $100. If the stakes were raised significantly, however, it would be worth my while sitting down with a pen and paper, going over the least convenient possible physical laws of the universe (that would then be known to me) and considering the problem in more depth. Discarding Quantum Mechanics in particular confuses me.
What I do assert with more confidence is that I would never wish to modify myself such that I made different decisions than I do. I would, rather, just make the decision itself.
I retract this statement. I have a suspicion that the addition of the ‘least convenient world’ criterion has overwhelmed my working memory with my current expertise in exotic decision making. I would need to think more on exactly what the implications are of novel restrictions before I could be confident.
I will say that in the situation you describe I would give $100. If the stakes were raised significantly, however, it would be worth my while sitting down with a pen and paper, going over the least convenient possible physical laws of the universe (that would then be known to me) and considering the problem in more depth. Discarding Quantum Mechanics in particular confuses me.
What I do assert with more confidence is that I would never wish to modify myself such that I made different decisions than I do. I would, rather, just make the decision itself.