As I know quite a bit about Functional Decision Theory (FDT), I’ll use FDT in my response. FDT two-boxes on CFC, but it doesn’t seem to me that’s wrong.
Tails Case
Omega modifies you such that you two-box. It does this by either giving you a two-boxing decision theory or by hard-coding some extra procedure that makes you two-box. E.g., Omega gives you FDT, which two-boxes. You two-box and make only $1,000, but what can you do? Run EDT? No, then Omega would have modified you into a two-boxer anyway. It’s not FDT’s mistake that you only make $1,000.
Heads Case
Omega modifies you such that you one-box. So you don’t run FDT (Omega makes you run a modified FDT or EDT or whatever). You make $1,000,000. Great!
The thing is, two-boxing isn’t wrong. If you two-box, then it was tails, and you indeed only make a $1,000, but that’s a consequence of the coin coming up tails, not of your decision. It wasn’t tails because of your decision to two-box. Your decision is completely redundant: in the tails case you always two-box, in the heads case you always one-box.
As I know quite a bit about Functional Decision Theory (FDT), I’ll use FDT in my response. FDT two-boxes on CFC, but it doesn’t seem to me that’s wrong.
Tails Case
Omega modifies you such that you two-box. It does this by either giving you a two-boxing decision theory or by hard-coding some extra procedure that makes you two-box. E.g., Omega gives you FDT, which two-boxes. You two-box and make only $1,000, but what can you do? Run EDT? No, then Omega would have modified you into a two-boxer anyway. It’s not FDT’s mistake that you only make $1,000.
Heads Case
Omega modifies you such that you one-box. So you don’t run FDT (Omega makes you run a modified FDT or EDT or whatever). You make $1,000,000. Great!
The thing is, two-boxing isn’t wrong. If you two-box, then it was tails, and you indeed only make a $1,000, but that’s a consequence of the coin coming up tails, not of your decision. It wasn’t tails because of your decision to two-box. Your decision is completely redundant: in the tails case you always two-box, in the heads case you always one-box.