I’m not sure where you get 3⁄2 expected decisions. Care to elaborate?
Here’s how I worked through i (ignoring expected decisions because I don’t think I understand that yet)t:
if you’re in the simulation, you get 260.
If you’re in reality day 1 (rd1), you lose 100 and expect to lose 100 on the next day
if you’re in reality day 2 (rd2), you lose 100
so 1/3(260-200-100) = −40/3
For rd1, if you give Omega the 100, then you know that when you wake up on rd2, you won’t recall giving Omega the 100. So you’ll be in exactly the same situation as you are right now, as far as you can tell. So you’ll give Omega the 100 again.
What’s wrong with the above reasoning? I’m not too experienced with game theoretic paradoxes, so my different line of reasoning probably means I’m wrong.
btw, If I attempt to calculate the expected decisions, I get 4⁄3
If Omega’s coin flip comes up heads, then you make one decision, to pay or not pay, as a simulation. If it comes up tails, then you make two decisions, to pay or not to pay, as a real person. These each have probability 0.5, so you expect to make 0.5(1+2)=1.5 decisions total.
The expected total value is the sum of the outcome for each circumstance times the expected number of times that circumstance is encountered. You can figure out the expected number of times each circumstance is encountered directly from the problem statement (0.5 for simulation, 0.5 for reality day 1, 0.5 for reality day 2). Alternatively, you can compute the expected number of times a circumstance C is encountered as P(individual decision is in C) E(decisions made), which is (1/3)(3/2), or 0.5, for simulation, reality day 1, and reality day 2. The mistake that Stuart_Armstrong made is in confusing E(times circumstance C is encountered) for P(individual decision is in C); these are not the same.
(Also, you double-counted the 100 you lose in reality day 2, messing up your expected value computation again.)
Apparently I had gestalt switched out of considering the coin. Thanks.
(Also, you double-counted the 100 you lose in reality day 2, messing up your expected value computation again.)
the double counting was intentional. My intuition was that if your on reality day 1, you expect to lose 100 today and 100 again tomorrow since you know you will give Omega the cash when he asks you. However, you don’t really know that in this thought experiment. He may give you amnesia, but he doesn’t get your brain in precisely the same physical state when he asks you the second time. So the problem seems resolved to me. This does suggest another thought experiment though.
I’m not sure where you get 3⁄2 expected decisions. Care to elaborate?
Here’s how I worked through i (ignoring expected decisions because I don’t think I understand that yet)t:
if you’re in the simulation, you get 260. If you’re in reality day 1 (rd1), you lose 100 and expect to lose 100 on the next day if you’re in reality day 2 (rd2), you lose 100
so 1/3(260-200-100) = −40/3
For rd1, if you give Omega the 100, then you know that when you wake up on rd2, you won’t recall giving Omega the 100. So you’ll be in exactly the same situation as you are right now, as far as you can tell. So you’ll give Omega the 100 again.
What’s wrong with the above reasoning? I’m not too experienced with game theoretic paradoxes, so my different line of reasoning probably means I’m wrong.
btw, If I attempt to calculate the expected decisions, I get 4⁄3
If Omega’s coin flip comes up heads, then you make one decision, to pay or not pay, as a simulation. If it comes up tails, then you make two decisions, to pay or not to pay, as a real person. These each have probability 0.5, so you expect to make 0.5(1+2)=1.5 decisions total.
The expected total value is the sum of the outcome for each circumstance times the expected number of times that circumstance is encountered. You can figure out the expected number of times each circumstance is encountered directly from the problem statement (0.5 for simulation, 0.5 for reality day 1, 0.5 for reality day 2). Alternatively, you can compute the expected number of times a circumstance C is encountered as P(individual decision is in C) E(decisions made), which is (1/3)(3/2), or 0.5, for simulation, reality day 1, and reality day 2. The mistake that Stuart_Armstrong made is in confusing E(times circumstance C is encountered) for P(individual decision is in C); these are not the same.
(Also, you double-counted the 100 you lose in reality day 2, messing up your expected value computation again.)
Apparently I had gestalt switched out of considering the coin. Thanks.
the double counting was intentional. My intuition was that if your on reality day 1, you expect to lose 100 today and 100 again tomorrow since you know you will give Omega the cash when he asks you. However, you don’t really know that in this thought experiment. He may give you amnesia, but he doesn’t get your brain in precisely the same physical state when he asks you the second time. So the problem seems resolved to me. This does suggest another thought experiment though.