what do you do about ideas which make identical predictions?
They get identical probabilities -- if their prior probabilities were equal.
If (as is the general practice around these parts) you give a markedly bigger prior probability to simpler hypotheses, then you will strongly prefer the simpler idea. (Here "simpler" means something like "when turned into a completely explicit computer program, has shorter source code". Of course your choice of language matters a bit, but unless you make wilfully perverse choices this will seldom be what decides which idea is simpler.)
In so far as the world turn...
Why expect AGIs to be better at thinking than human beings? Is there some argument that human thinking problems are primarily due to hardware constraints? Has anyone here put much thought into parenting/educating AGIs?