Somewhere in between? I have reliable intuition about what would happen that comes before being able to construct the proof, but can reliably be turned into the proof. All of the proofs that these agents do what I say they do can be found by asking:
Assume that the probability does not converge as I say it does. How can I use this to make money if I am allowed to see (continuously) the logical inductors beliefs, and bet against them?
For example in the first example, If the probability was greater that 1/2+δ infinity often, I could wait until the probability is greater than 1/2+δ, then bet that the agent goes right. This bet will always pay out, and double my money, and I can do this forever.
Somewhere in between? I have reliable intuition about what would happen that comes before being able to construct the proof, but can reliably be turned into the proof. All of the proofs that these agents do what I say they do can be found by asking:
Assume that the probability does not converge as I say it does. How can I use this to make money if I am allowed to see (continuously) the logical inductors beliefs, and bet against them?
For example in the first example, If the probability was greater that 1/2+δ infinity often, I could wait until the probability is greater than 1/2+δ, then bet that the agent goes right. This bet will always pay out, and double my money, and I can do this forever.