I’ll modify my advice. If the probability that “I do action A in order to increase my subjective probability of position P” is greater given P than given not P, then doing A in order to increase my subjective probability of position P will be evidence in favor of P.
So in many cases, there will such a plan that I can devise. Let’s see Eliezer find a way out of this one.
Before you have actually done A, since it might fail because of ~P (which is what the thing you said actually means), your confidence is still the same as before you came up with the plan. We’re still at t=0. Information about your plan succeeding or not hasn’t arrived yet.
Now if over the course of planning you realize that the very ability you have to make the plan shifts probability estimate of P, then we’ve already got the new evidence. We’re at t=1, and the probability has shifted rightfully without violating the law. The evidence is no longer expected, it’s already here!
Before you started planning, you didn’t know that you would succeed and get this information. Not for certain. Or if you did, your estimate of probability of P was clearly wrong, but you hadn’t noticed it yet, where the “yet” is the time factor that distinguishes between t0 and t1 again...
Can’t cheat your way out of this at t=0, I’m afraid.
Let’s say you are organising a polar expedition. It will succeed (A) or fail (~A). There is a postulate that there are no man eating polar Cthulhu in the area (P). If there are some (~P), the expedition will fail (~A), thus entangling A with P.
You can do your best to prepare the expedition so that it will not fail for non-Cthulhu reasons, strengthening the entanglement - ~A becomes stronger evidence for ~P. You can also do your best to prepare the expedition to survive even the man eating polar Cthulhu, weakening the entanglement—by introducing a higher probability of A&~P, we’re making A weaker evidence for P.
Do any of these preparations, in themselves, actually influence the amount of man eating polar Cthulhu in the area?
I’ll modify my advice. If the probability that “I do action A in order to increase my subjective probability of position P” is greater given P than given not P, then doing A in order to increase my subjective probability of position P will be evidence in favor of P.
So in many cases, there will such a plan that I can devise. Let’s see Eliezer find a way out of this one.
Before you have actually done A, since it might fail because of ~P (which is what the thing you said actually means), your confidence is still the same as before you came up with the plan. We’re still at t=0. Information about your plan succeeding or not hasn’t arrived yet.
Now if over the course of planning you realize that the very ability you have to make the plan shifts probability estimate of P, then we’ve already got the new evidence. We’re at t=1, and the probability has shifted rightfully without violating the law. The evidence is no longer expected, it’s already here!
Before you started planning, you didn’t know that you would succeed and get this information. Not for certain. Or if you did, your estimate of probability of P was clearly wrong, but you hadn’t noticed it yet, where the “yet” is the time factor that distinguishes between t0 and t1 again...
Can’t cheat your way out of this at t=0, I’m afraid.
Let’s say you are organising a polar expedition. It will succeed (A) or fail (~A). There is a postulate that there are no man eating polar Cthulhu in the area (P). If there are some (~P), the expedition will fail (~A), thus entangling A with P.
You can do your best to prepare the expedition so that it will not fail for non-Cthulhu reasons, strengthening the entanglement - ~A becomes stronger evidence for ~P. You can also do your best to prepare the expedition to survive even the man eating polar Cthulhu, weakening the entanglement—by introducing a higher probability of A&~P, we’re making A weaker evidence for P.
Do any of these preparations, in themselves, actually influence the amount of man eating polar Cthulhu in the area?