jimrandomh comments on Omega’s subcontracting to Alpha

[jimrandomh]

This program must be embedded in a larger one, since the original problem description didn’t say what Omega would do if it couldn’t truthfully make the prediction it did. Call that larger program U2(S). The only thing we are told about U2 is that it only calls U if it can do so in a way which guarantees that U won’t reach a contradiction. Suppose, for example, that if Omega’s prediction couldn’t be made truthfully then you wouldn’t get any money at all. This corresponds to the world program:

U2(S) =
{
    try {
        return U(S)
    } catch(contradiction) {
        return 0
    }
}

Note that there are plenty of mathematically equivalent ways to write this—for example, using a would_throw(U,S,RNG) function.