The usual formulations typically have Omega being “bigger” than your agent, such that Omega can predict your agent, but your agent cannot predict Omega. This is generally taken to be unproblematic because physical agents are always bounded by time + memory constraints, which makes them analogous to finite-state machines rather than full Turing machines. (If unbounded computation were permitted, on the other hand, then you would indeed need a super-Turing version of Omega to pull off the trick.)
Paradoxical decision problems are paradoxical in the colloquial sense (such as Hilbert’s hotel or Bertrand’s paradox), not the literal sense (such as “this sentence is false”). Paradoxicality is in the eye of the beholder. Some people think Newcomb’s problem is paradoxical, some don’t. I agree with you and don’t find it paradoxical.
In that case why are people spending so much effort on it[1]?
Ditto, why is there so much argumentation based around applying game theory to Newcomb’s problem[2] (or variants) when much of game theory does not apply to it?
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Paradoxical decision problems are paradoxical in the colloquial sense (such as Hilbert’s hotel or Bertrand’s paradox), not the literal sense (such as “this sentence is false”).
I think that there is a lot of effort being wasted due to not clearly distinguishing counterintuative results and self-contradictory results in general, and this is a prime example.
Such as “Evidential decision theories are inadequate rational decision theories. For either they provide wrong solutions to Newcomb’s problem [...]”, which is a direct quote from the overview of Newcomb’s problem linked in the description of the tag ‘Newcomb’s Problem’ on this site.
The usual formulations typically have Omega being “bigger” than your agent, such that Omega can predict your agent, but your agent cannot predict Omega. This is generally taken to be unproblematic because physical agents are always bounded by time + memory constraints, which makes them analogous to finite-state machines rather than full Turing machines. (If unbounded computation were permitted, on the other hand, then you would indeed need a super-Turing version of Omega to pull off the trick.)
...in which case much of game theory does not apply and the paradoxes, by and large, aren’t actually paradoxical, no?
Paradoxical decision problems are paradoxical in the colloquial sense (such as Hilbert’s hotel or Bertrand’s paradox), not the literal sense (such as “this sentence is false”). Paradoxicality is in the eye of the beholder. Some people think Newcomb’s problem is paradoxical, some don’t. I agree with you and don’t find it paradoxical.
In that case why are people spending so much effort on it[1]?
Ditto, why is there so much argumentation based around applying game theory to Newcomb’s problem[2] (or variants) when much of game theory does not apply to it?
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I think that there is a lot of effort being wasted due to not clearly distinguishing counterintuative results and self-contradictory results in general, and this is a prime example.
The LessWrong “Newcomb’s Problem” tag has 41 entries with a combined total of over 1,000 comments, for instance.
See also any argument[3] that says that X is invalid because it provides ‘the wrong solution’ to Newcomb’s Problem.
Such as “Evidential decision theories are inadequate rational decision theories. For either they provide wrong solutions to Newcomb’s problem [...]”, which is a direct quote from the overview of Newcomb’s problem linked in the description of the tag ‘Newcomb’s Problem’ on this site.