So, those still reading, you would give Omega the $100.
It’s a little too strong, I think you shouldn’t give away the $100, because you are just not reflectively consistent. It’s not you who could’ve ran the expected utility calculation to determine that you should give it away. If you persist, by the time you must do the action it’s not in your interest anymore, it’s a lost cause. And that is a subject of another post that has been lying in draft form for some time.
If you are strong enough to be reflectively consistent, then …
In short, what information do you use to calculate the probability you plug into the EU calculation?
You use your prior for probabilistic valuation, structured to capture expected subsequent evidence on possible branches. According to evidence and possible decisions on each branch, you calculate expected utility of all of the possible branches, find a global feasible maximum, and perform a component decision from it that fits the real branch. The information you have doesn’t directly help in determining the global solution, it only shows which of the possible branches you are on, and thus which role should you play in the global decision, that mostly applies to the counterfactual branches. This works if the prior/utility is something inside you, worse if you have to mine information from the real branch for it in the process. Or, for more generality, you can consider yourself cooperating with your counterfactual counterparts.
The crux of the problem is that you care about counterfactuals; once you attain this, the rest is business as usual. When you are not being reflectively consistent, you let the counterfactual goodness slip away from your fingers, turning to myopically optimizing only what’s real.
It’s a little too strong, I think you shouldn’t give away the $100, because you are just not reflectively consistent. It’s not you who could’ve ran the expected utility calculation to determine that you should give it away. If you persist, by the time you must do the action it’s not in your interest anymore, it’s a lost cause. And that is a subject of another post that has been lying in draft form for some time.
If you are strong enough to be reflectively consistent, then …
You use your prior for probabilistic valuation, structured to capture expected subsequent evidence on possible branches. According to evidence and possible decisions on each branch, you calculate expected utility of all of the possible branches, find a global feasible maximum, and perform a component decision from it that fits the real branch. The information you have doesn’t directly help in determining the global solution, it only shows which of the possible branches you are on, and thus which role should you play in the global decision, that mostly applies to the counterfactual branches. This works if the prior/utility is something inside you, worse if you have to mine information from the real branch for it in the process. Or, for more generality, you can consider yourself cooperating with your counterfactual counterparts.
The crux of the problem is that you care about counterfactuals; once you attain this, the rest is business as usual. When you are not being reflectively consistent, you let the counterfactual goodness slip away from your fingers, turning to myopically optimizing only what’s real.