Running through this to check that my wetware handles it consistently.
Paying −100 if asked:
When the coin is flipped, one’s probability branch splits into a 0.5 of oneself in the ‘simulation’ branch, 0.5 in the ‘real’ branch. For the 0.5 in the real branch, upon awaking a subjective 50% probability that on either of the two possible days, both of which will be woken on. So, 0.5 of the time waking in simulation, 0.25 waking in real 1, 0.25 waking in real 2.
0.5 x (260) + 0.25 x (-100) + 0.25 x (-100) = 80. However, this is the expected cash-balance change over the course of a single choice, and doesn’t take into account that Omega is waking you multiple times for the worse choice.
An equation for relating choice made to expected gain/loss at the end of the experiment doesn’t ask ‘What is my expected loss according to which day in reality I might be waking up in?‘, but rather only ‘What is my expected loss according to which branch of the coin toss I’m in?’ 0.5 x (260) + 0.5 x (-100-100) = 30.
Another way of putting it: 0.5 x (260) + 0.25 x (-100(-100)) + 0.25 x (-100(-100)) = 30
(Given that making one choice in a 0.25 branch guarantees the same choice made, separated by a memory-partition; either you’ve already made the choice and don’t remember it, or you’re going to make the choice and won’t remember this one, for a given choice that the expected gain/loss is being calculated for. The ‘-100’ is the immediate choice that you will remember (or won’t remember), the ‘(-100)’ is the partition-separated choice that you don’t remember (or will remember).)
--Trying to see what this looks like for an indefinite number of reality wakings:
0.5 * (260) + n x (1/n) x (1/2) x (-100 x n) = 130 - (50 x n), which of the form that might be expected.
(Edit: As with reddit, frustrating that line breaks behave differently in the commenting field and the posted comment.)
Running through this to check that my wetware handles it consistently.
Paying −100 if asked:
When the coin is flipped, one’s probability branch splits into a 0.5 of oneself in the ‘simulation’ branch, 0.5 in the ‘real’ branch. For the 0.5 in the real branch, upon awaking a subjective 50% probability that on either of the two possible days, both of which will be woken on. So, 0.5 of the time waking in simulation, 0.25 waking in real 1, 0.25 waking in real 2.
0.5 x (260) + 0.25 x (-100) + 0.25 x (-100) = 80. However, this is the expected cash-balance change over the course of a single choice, and doesn’t take into account that Omega is waking you multiple times for the worse choice.
An equation for relating choice made to expected gain/loss at the end of the experiment doesn’t ask ‘What is my expected loss according to which day in reality I might be waking up in?‘, but rather only ‘What is my expected loss according to which branch of the coin toss I’m in?’ 0.5 x (260) + 0.5 x (-100-100) = 30.
Another way of putting it: 0.5 x (260) + 0.25 x (-100(-100)) + 0.25 x (-100(-100)) = 30 (Given that making one choice in a 0.25 branch guarantees the same choice made, separated by a memory-partition; either you’ve already made the choice and don’t remember it, or you’re going to make the choice and won’t remember this one, for a given choice that the expected gain/loss is being calculated for. The ‘-100’ is the immediate choice that you will remember (or won’t remember), the ‘(-100)’ is the partition-separated choice that you don’t remember (or will remember).)
--Trying to see what this looks like for an indefinite number of reality wakings: 0.5 * (260) + n x (1/n) x (1/2) x (-100 x n) = 130 - (50 x n), which of the form that might be expected.
(Edit: As with reddit, frustrating that line breaks behave differently in the commenting field and the posted comment.)