Something about your proposed decision problem seems cheaty in a way that the standard Newcomb problem doesn’t. I’m not sure exactly what it is, but I will try to articulate it, and maybe you can help me figure it out.
It reminds me of two different decision problems. Actually, the first one isn’t really a decision problem.
Omega has decided to give all those who two box on the standard Newcomb problem 1,000,000 usd, and all those who do not 1,000 usd.
Now that’s not really a decision problem, but that’s not the issue with using it to decide between decision theories. I’m not sure exactly what the issue is but it seems like it is not the decisions of the agent that make the world go one way or the other. Omega could also go around rewarding all CDT agents and punishing all FDT agents, but that wouldn’t be a good reason to prefer CDT. It seems like in your problem it is not the decision of the agent that determines what their payout is, whereas in the standard newcomb problem it is. Your problem seems more like a scenario where omega goes around punishing agents with a particular decision theory than one where an agent’s decisions determine their payout.
Now there’s another decision problem this reminds me of.
Omega flips a coin and tell you “I flipped a coin, and I would have paid you 1,000,000 usd if it came up heads only if I predicted that you would have paid me 1,000 usd if it came up tails after having this explained to you. The coin did in fact come up tails. Will you pay me?”
In this decision problem your payout also depends on what you would have done in a different hypothetical scenario, but it does not seem cheaty to me in the same way your proposed decision problem does. Maybe that is because it depends on what you would have done in this same problem had a different part of it gone differently.
I’m honestly not sure what I am tracking when I judge whether a decision problem is cheaty or not (where cheaty just means “should be used to decide between decision theories”) but I am sure that your problem seems cheaty to me right now. Do you have any similar intuitions or hunches about what I am tracking?
I think I see where you’re coming from with the inverse problem feeling “cheaty”. It’s not like other decision problems in the sense that it is not really a dilemma; two-boxing is clearly the best option. I used the word “problem” instinctively, but perhaps I should have called it the “Inverse Newcomb Scenario” or something similar instead.
However, the fact that it isn’t a real “problem” doesn’t change the conclusion. I admit that the inverse scenario is not as interesting as the standard problem, but what matters is that it’s just as likely, and clearly favours two-boxers. FDT agents have a pre-commitment to being one-boxers, and that would work well if the universe actually complied and provided them with the scenario they have prepared for (which is what the paper seems to assume). What I tried to show with the inverse scenario is that it’s just as likely that their pre-commitment to one-boxing will be used against them.
Both Newcomb’s Problem and the Inverse Scenario are “unfair” for one of the theories, which is why I think the proper performance measure is the total money for going through botha, where CDT comes out on top.
Something about your proposed decision problem seems cheaty in a way that the standard Newcomb problem doesn’t. I’m not sure exactly what it is, but I will try to articulate it, and maybe you can help me figure it out.
It reminds me of two different decision problems. Actually, the first one isn’t really a decision problem.
Omega has decided to give all those who two box on the standard Newcomb problem 1,000,000 usd, and all those who do not 1,000 usd.
Now that’s not really a decision problem, but that’s not the issue with using it to decide between decision theories. I’m not sure exactly what the issue is but it seems like it is not the decisions of the agent that make the world go one way or the other. Omega could also go around rewarding all CDT agents and punishing all FDT agents, but that wouldn’t be a good reason to prefer CDT. It seems like in your problem it is not the decision of the agent that determines what their payout is, whereas in the standard newcomb problem it is. Your problem seems more like a scenario where omega goes around punishing agents with a particular decision theory than one where an agent’s decisions determine their payout.
Now there’s another decision problem this reminds me of.
Omega flips a coin and tell you “I flipped a coin, and I would have paid you 1,000,000 usd if it came up heads only if I predicted that you would have paid me 1,000 usd if it came up tails after having this explained to you. The coin did in fact come up tails. Will you pay me?”
In this decision problem your payout also depends on what you would have done in a different hypothetical scenario, but it does not seem cheaty to me in the same way your proposed decision problem does. Maybe that is because it depends on what you would have done in this same problem had a different part of it gone differently.
I’m honestly not sure what I am tracking when I judge whether a decision problem is cheaty or not (where cheaty just means “should be used to decide between decision theories”) but I am sure that your problem seems cheaty to me right now. Do you have any similar intuitions or hunches about what I am tracking?
I think I see where you’re coming from with the inverse problem feeling “cheaty”. It’s not like other decision problems in the sense that it is not really a dilemma; two-boxing is clearly the best option. I used the word “problem” instinctively, but perhaps I should have called it the “Inverse Newcomb Scenario” or something similar instead.
However, the fact that it isn’t a real “problem” doesn’t change the conclusion. I admit that the inverse scenario is not as interesting as the standard problem, but what matters is that it’s just as likely, and clearly favours two-boxers. FDT agents have a pre-commitment to being one-boxers, and that would work well if the universe actually complied and provided them with the scenario they have prepared for (which is what the paper seems to assume). What I tried to show with the inverse scenario is that it’s just as likely that their pre-commitment to one-boxing will be used against them.
Both Newcomb’s Problem and the Inverse Scenario are “unfair” for one of the theories, which is why I think the proper performance measure is the total money for going through botha, where CDT comes out on top.