Reference Post: Formal vs. Effective Pre-Commitment

Not sure why people find the Newcomb's problem so complicated, it is pretty trivial: you one-box: you win, you two-box: you lose. Doesn't matter when you feel you have made the decision, either, what maters is the decision itself. The confusion arises when people try to fight the hypothetical by assuming an impossible world where they can fool a perfect predictor has a non-zero probability of becoming an actual world.

In particular, I'd argue that the paradoxical aspects of Newcomb's problem result from exactly this kind of confusion between the usual agent idealization and the fact that actual actors (human beings) are physical beings subject to the laws of physics. The apparent paradoxical aspects results because we are used to idealizing individual behavior in terms of agents where that formalism requires we specify the situation in terms of a tree of possibilities with each path corresponding to an outcome and with the payoff computed by looking at the path specified by all agent's choices (e.g. there is a node where the demon player chooses what money to put in the boxes and then there is a node where the human player, without knowledge of demon player's choices, decides to take both boxes or neither). The agent formalization (where 1 or 2 boxing is modeled as a subsequent choice) simply doesn't allow the content of the boxes to depend on whether or not the human agent chooses 1 or 2 boxes.

Of course, since actual people aren't ideal agents one can argue that something like the newcomb demon is physically possible but that's just a way of specifying that we are in a situation where the agent idealization breaks down.

This means there is simply no fact of the matter about how a rational agent (or whatever) should behave in newcomb type situations because the (usual) rational agent idealization is incompatible with the newcomb situation (ok, more technically you can model it that way but the choice of how to model it just unsatisfactorily builds in the answer by specifying how the payoff depends on 1 vs two boxing).

To sum up what the answer to the newcomb problem is depends heavily on how you preciscify the question. Are you asking whether humans who are disposed to decide in way A end up better of than humans disposed to behave in way B? In that case it's easy. But things like CDT, TDT etc.. don't claim to be producing facts of that kind but rather saying something about ideal rational agents of some kind which then just boringly depends on a ambiguities in what we mean by that.ideal rational agents.

I'd argue that nobody cares about formal pre-commitments, except to the extent that formality increases knowledge of effective pre-committments.

typo: "Casual Decision Theory"

True Path has already covered it (or most of it) extensively, but both the Newcomb's Problem and the distinction made in the post (if it were to be applied in a game theory setting) contain too many inherent contradiction and do not seem to actually point out anything concrete.

You can't talk about decision-making agents if they are basically not making any decisions (classical determinism, or effective precommitment in this case, enforces that). Also, you can't have a 100% accurate predictor and have freedom of choice on the other hand, because that implies (in the very least) that the subset of phenomena in the universe that govern your decision is deterministic.

[Plus, even if you have a 99.9999... (... meaning some large N times 9, not infinity) percent accurate predictor, if the Newcomb's problem assumes perfect rationality, there's really no paradox.

I think what this post exemplifies (and perhaps that was the intent from the get-go and I just completely missed it) is precisely that Newcomb's is ambiguous about the type of precommitment taken (which follows from it being ambiguous about how Omega works) and therefore is sort of self contradictory, and not truly a paradox.]

It doesn't really make sense to talk about the agent idealization at the same time as talking about effective precommitment (i.e. deterministic/probabilistic determination of actions).

The notion of an agent is an idealization of actual actors in terms of free choices, e.g., idealizing individuals in terms of choices of functions on game theoretic trees. This is an incompatible idealization with thinking of such actors as being deterministically or probabilistically committed to actions for those same 'choices.'

Of course, ultimately, actual actors (e.g. people) are only approximated by talk of agents but if you try and simultaneously use the agent idealization while regarding those *same* choices as being effectively precommited you risk contradiction and model absurdity (of course you can decide to reduce the set of actions you regard as free choices in the agent idealization but that doesn't seem to be the way you are talking about things here).

Some people, like detectives or poker players, may be really good at reading people, but they're still nothing compared to a perfect predictor and most people aren't even this good.

Which is why the notion of trust exists - if someone always does something (they're never late), we figure they will probably continue to do so. The longer a pattern holds, the more credence we lend to it continuing (especially if it's very consistent).