Infinite copies of you may each spend 1 point. If #1 does, everyone gains 2 points. Equipped with the Self-Importance Assumption that we are >50% likely to be #1, CDT acts like UDT.
Suppose we modify the game so that you can now spend 1 point on the “if you’re #1, everyone gets 2 points” gamble, and also can choose to spend 1 point on the “if you’re #1, you get 2 points” gamble. UDT still is fine, self-important CDT loses all its gains. I feel like the moral of the story is “just don’t be CDT.”
You’re right! My own search for counterarguments only came as far as “as the amount of points everyone gains decreases to 1, the probability of #1 required to match UDT rises to 1”—I didn’t manage to leave the parameter space I’d constructed, to prove myself wrong.
And yet. Yes, for any probabilities, CDT will take the one action iff it takes the other, and UDT has some probability distribution (used to weight each copy’s utility) such that it takes one action but not the other. Does every game have a probability distribution where CDT and UDT agree? Can we naturally construct a sane such anthropic assumption? The utility function isn’t up for grabs, but this’d still seems like a hint.
Infinite copies of you may each spend 1 point. If #1 does, everyone gains 2 points. Equipped with the Self-Importance Assumption that we are >50% likely to be #1, CDT acts like UDT.
Suppose we modify the game so that you can now spend 1 point on the “if you’re #1, everyone gets 2 points” gamble, and also can choose to spend 1 point on the “if you’re #1, you get 2 points” gamble. UDT still is fine, self-important CDT loses all its gains. I feel like the moral of the story is “just don’t be CDT.”
You’re right! My own search for counterarguments only came as far as “as the amount of points everyone gains decreases to 1, the probability of #1 required to match UDT rises to 1”—I didn’t manage to leave the parameter space I’d constructed, to prove myself wrong.
And yet. Yes, for any probabilities, CDT will take the one action iff it takes the other, and UDT has some probability distribution (used to weight each copy’s utility) such that it takes one action but not the other. Does every game have a probability distribution where CDT and UDT agree? Can we naturally construct a sane such anthropic assumption? The utility function isn’t up for grabs, but this’d still seems like a hint.