I'm sure I remember reading somewhere that an informal slogan for (some brand of decision theory) was:

"Act in accordance with the precommittment you wish you had made."

i.e. when faced with Newcomb's problem, you would wish you had precommitted to one-box, and so you should one-box. This is entirely predictable, so you get the money.

However, I couldn't find where I saw this, and I can't remember which decision theory it was meant to exemplify - and I don't actually understand the maths of the various competitors enough to figure out which it is.

Could someone who knows the area better point me in the right direction? In general, the idea of making a kind of "fully general precommitment" seems like an intuitive way of explaining how you can improve on, say, CDT.

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I am not a decision theorist, but that quote is the original statement of TDT, Eliezers Timeless Decision Theory.

Yep, that sounds like TDT.

It's also similar to my slogan form of UDT ("updateless decision theory") which is "Find the strategy that gives the best payoff, then follow that strategy."