cousin_it comments on Timeless Decision Theory: Problems I Can't Solve

27Eliezer_Yudkowsky20 July 2009 12:02AM

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cousin_it28 December 2009 08:58:27PM* 2 points [-]

Here's a comment that took me way too long to formulate:

On the Prisoner's Dilemma in particular, this infinite regress can be cut short by expecting that the other agent is doing symmetrical reasoning on a symmetrical problem and will come to a symmetrical conclusion...

Eliezer, if such reasoning from symmetry is allowed, then we sure don't need your "TDT" to solve the PD!

Eliezer_Yudkowsky28 December 2009 10:47:04PM* 2 points [-]

TDT allows you to use whatever you can prove mathematically. If you can prove that two computations have the same output because their global structures are isomorphic, it doesn't matter if the internal structure is twisty or involves regresses you haven't yet resolved. However, you need a license to use that sort of mathematical reasoning in the first place, which is provided by TDT but not CDT.

Perplexed01 August 2010 12:39:49AM0 points [-]

Strategies are probability (density) functions over choices. Behaviors are the choices themselves. Proving that two strategies are identical (by symmetry, say) doesn't license you to assume that the behaviors are the same. And it is behaviors you seem to need here. Two random variables over the same PDF are not equal.

Seldin got a Nobel for re-introducing time into game theory (with the concept of subgame perfect equilibrium as a refinement of Nash equilibrium). I think he deserved the prize. If you think that you can overturn Seldin's work with your TDT, then I say "To hell with a PhD. Write it up and go straight to Stockholm."

Sniffnoy03 August 2010 04:51:28AM0 points [-]

Strategies are probability (density) functions over choices. Behaviors are the choices themselves. Proving that two strategies are identical (by symmetry, say) doesn't license you to assume that the behaviors are the same.

...unless the resulting strategies are unmixed, as will usually be the case with Prisoner's Dilemma?