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Nick_Tarleton comments on Decision theory: Why Pearl helps reduce “could” and “would”, but still leaves us with at least three alternatives - Less Wrong
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Comments (70)
Agents do not need to calculate what would have happened, if something impossible had happened.
They need to calculate the consequences of their possible actions.
These are all possible, by definition, from the point of view of the agent - who is genuinely uncertain about the action she is going to take. Thus, from her point of view at the time, these scenarios are not "counterfactual". They do not contradict any facts known to her at the time. Rather they all lie within her cone of uncertainty.
... but nevertheless, all but one are, in fact, logically impossible.
That's the difference between epistemic and metaphysical possibility. Something can be epistemically possible without being metaphysically possible if one doesn't know if it's metaphysically possible or not.
Thanks, that's exactly what I was trying to say.
What do you mean?
Are you perhaps thinking of a type of classical determinism - that pre-dates the many-worlds perspective...?
I'm thinking of determinism. I don't know what you mean by "classical" or in what way you think many-worlds is non-"classically"-deterministic (or has any bearing on decision theory).
If all your possible actions are realised in a future multiverse of possibilities, it is not really true that all but one of those actions is "logically impossible" at the point when the decision to act is taken.
Many-worlds doesn't have a lot to do with decision theory - but it does bear on your statement about paths not taken being "impossible".
Actually, the way that TDT defines a decision, only one decision is ever logically possible, even under many-worlds. Versions of you that did different things must have effectively computed a different decision-problem.
Worlds can split before a decision - but they can split 1 second before, 1 millisecond before - or while the decision to be made is still being evaluated.
So? Versions of you that choose different strategies must have ended up performing different computations due to splits at whatever time, hence, under TDT, one decision-process still only makes one decision.