I’m still not convinced. Suppose an agent has to play a game: two rounds of Russian roulette with a revolver with one bullet and N chambers. The agent doesn’t know N, and will get a reward R if they survive both rounds; if they give up after one round, they get a consolation prize C1 < R. If they give up immediately, they get one C0 < C1 < R.
The optimal strategy depends on N, and the agent’s belief about it. The question is, suppose the agent already passed the first round, and survived, does this give them any information about the distribution P(N)? Anthropic shadow says “no” because, conditioned on them having any use for the information, they must also have survived the first round. So I suppose you could reframe the anthropic shadow as a sort of theorem about how much useful information you can extract out of the outcomes of a series of past rounds of a game in which loss limits your future actions (death being one extreme outcome). I need to think about formalizing this.
And it is wrong because the anthropic principle is true: we learned that N ≠ 1.
Fair, but no more. And any additional survival doesn’t teach us anything else. All meaningful information only reaches us once we have no more use for it.
I’m still not convinced. Suppose an agent has to play a game: two rounds of Russian roulette with a revolver with one bullet and N chambers. The agent doesn’t know N, and will get a reward R if they survive both rounds; if they give up after one round, they get a consolation prize C1 < R. If they give up immediately, they get one C0 < C1 < R.
The optimal strategy depends on N, and the agent’s belief about it. The question is, suppose the agent already passed the first round, and survived, does this give them any information about the distribution P(N)? Anthropic shadow says “no” because, conditioned on them having any use for the information, they must also have survived the first round. So I suppose you could reframe the anthropic shadow as a sort of theorem about how much useful information you can extract out of the outcomes of a series of past rounds of a game in which loss limits your future actions (death being one extreme outcome). I need to think about formalizing this.
And it is wrong because the anthropic principle is true: we learned that N ≠ 1.
There is the idea of Anthropic decision theory which is related, but I’m still guessing it still has no shadow.
Fair, but no more. And any additional survival doesn’t teach us anything else. All meaningful information only reaches us once we have no more use for it.