Your expected bayes factor is necessarily 1 weighted over your prior; you expect to find evidence for neither side.
I think this claim is correct on the natural scale except it should be weighted over probability of the data, not weighted over the prior. The margin of this comment is too small to contain the proof, so I’ll put a pdf in my public drop box folder at https://www.dropbox.com/s/vmom25u9ic7redu/Proof.pdf?dl=0
(I am slightly out of my depth here, I am not a mathematician or a Bayesian theorist, so I reserve the right to delete this comment if someone spots a flaw)
I think this claim is correct on the natural scale except it should be weighted over probability of the data, not weighted over the prior. The margin of this comment is too small to contain the proof, so I’ll put a pdf in my public drop box folder at https://www.dropbox.com/s/vmom25u9ic7redu/Proof.pdf?dl=0
(I am slightly out of my depth here, I am not a mathematician or a Bayesian theorist, so I reserve the right to delete this comment if someone spots a flaw)