This variation of the problem was invented in the follow-up post (I think it was called “Sneaky strategies for TDT” or something like that:
Omega tells you that earlier he flipped a coin. If the coin came down heads, it simulated a CDT agent facing this problem. If the coin came down tails, it simulated a TDT agent facing this problem. In either case, if the simulated agent one-boxed, there is $1000000 in Box-B; if it two-boxed Box-B is empty. In this case TDT still one-boxes (50% chance of $1000000 dominates a 100% chance of $1000), and CDT still two-boxes (because that’s what CDT does). In this case, even though both agents have an equal chance of being simulated, CDT out-performs TDT (average payoffs of 500500 vs. 500000) - CDT takes advantage of TDT’s prudence and TDT suffers for CDT’s lack of it. Notice also that TDT cannot do better by behaving like CDT (both would get payoffs of 1000). This shows that the class of problems we’re concerned with is not so much “fair” vs. “unfair”, but more like “those problem on which the best I can do is not necessarily the best anyone can do”. We can call it “fairness” if we want, but it’s not like Omega is discriminating against TDT in this case.
This is not a zero-sum game. CDT does not outperform TDT here. It just makes a stupid mistake, and happens to pay it less dearly than TDT
Let’s say Omega submit the same problem to 2 arbitrary decision theories. Each will either 1-box or 2-box. Here is the average payoff matrix:
Both a and b 1-box → They both get the million
Both a and b 2-box → They both get 1000 only.
One 1-boxes, the other 2-boxes → the 1-boxer gets half a million, the other gets 5000 more.
Clearly, 1 boxing still dominates 2-boxing. Whatever the other does, you personally get about half a million more by 1-boxing. TDT may have less utility than CDT for 1-boxing, but CDT is still stupid here, while TDT is not.
This variation of the problem was invented in the follow-up post (I think it was called “Sneaky strategies for TDT” or something like that:
Omega tells you that earlier he flipped a coin. If the coin came down heads, it simulated a CDT agent facing this problem. If the coin came down tails, it simulated a TDT agent facing this problem. In either case, if the simulated agent one-boxed, there is $1000000 in Box-B; if it two-boxed Box-B is empty. In this case TDT still one-boxes (50% chance of $1000000 dominates a 100% chance of $1000), and CDT still two-boxes (because that’s what CDT does). In this case, even though both agents have an equal chance of being simulated, CDT out-performs TDT (average payoffs of 500500 vs. 500000) - CDT takes advantage of TDT’s prudence and TDT suffers for CDT’s lack of it. Notice also that TDT cannot do better by behaving like CDT (both would get payoffs of 1000). This shows that the class of problems we’re concerned with is not so much “fair” vs. “unfair”, but more like “those problem on which the best I can do is not necessarily the best anyone can do”. We can call it “fairness” if we want, but it’s not like Omega is discriminating against TDT in this case.
This is not a zero-sum game. CDT does not outperform TDT here. It just makes a stupid mistake, and happens to pay it less dearly than TDT
Let’s say Omega submit the same problem to 2 arbitrary decision theories. Each will either 1-box or 2-box. Here is the average payoff matrix:
Both a and b 1-box → They both get the million
Both a and b 2-box → They both get 1000 only.
One 1-boxes, the other 2-boxes → the 1-boxer gets half a million, the other gets 5000 more.
Clearly, 1 boxing still dominates 2-boxing. Whatever the other does, you personally get about half a million more by 1-boxing. TDT may have less utility than CDT for 1-boxing, but CDT is still stupid here, while TDT is not.