Oh, and if the special circumstances offered to AIXI are a problem w.r.t. allowing tricky explanations, I think that should be resolvable.
For example, getting to watch other agents play before making your own decision is the “VIP treatment”. Omega decides whether or not to give this treatment by transparently by generating a pseudorandom integer between 1 and 2000, and it gives the VIP treatment if and only if that integer comes up as a 1. The player gets to directly observe the random number generation mechanism while Omega is using it.
Out of the 1000 agents who also got to play Omega’s game while AIXI was watching, a 1 came up on the 965th game. When that happened, that agent got to watch 1000 games, although in those 1000 a 1 didn’t come up at all. Since AIXI was still waiting around, it got to watch those extra 1000 games before watching the last 35 games of its VIP allocation. Of the 2000 games played, Omega made 2000 correct predictions.
If 2000/2000 is too unlikely and inherently results in weird explanations, we can adjust the number down appropriately e.g. 1900/2000.
Oh, and if the special circumstances offered to AIXI are a problem w.r.t. allowing tricky explanations, I think that should be resolvable.
For example, getting to watch other agents play before making your own decision is the “VIP treatment”. Omega decides whether or not to give this treatment by transparently by generating a pseudorandom integer between 1 and 2000, and it gives the VIP treatment if and only if that integer comes up as a 1. The player gets to directly observe the random number generation mechanism while Omega is using it.
Out of the 1000 agents who also got to play Omega’s game while AIXI was watching, a 1 came up on the 965th game. When that happened, that agent got to watch 1000 games, although in those 1000 a 1 didn’t come up at all. Since AIXI was still waiting around, it got to watch those extra 1000 games before watching the last 35 games of its VIP allocation. Of the 2000 games played, Omega made 2000 correct predictions.
If 2000/2000 is too unlikely and inherently results in weird explanations, we can adjust the number down appropriately e.g. 1900/2000.