According to the Bayesian interpretation of ECREE, the relevant probabilities are to be understood as epistemic probabilities (as opposed to the classical, logical, or other interpretations of probability). So the objector is correct that the Bayesian interpretation is inherently subjective in the sense that it depends entirely upon what a person knows and believes. So what? It doesn't follow that we can't figure out what are extraordinary claims.
As we shall we see below, we use the same formula for both ordinary and extraordinary claims to determine the evidence required to establish a high final probability for a claim…Notice that the inequalities are the same for both ordinary and extraordinary evidence. This might lead one to wonder, "Then why bother with the ECREE slogan at all?" The answer is this. ECREE emphasizes the common sense notion that the more implausible we initially regard a claim prior to considering the evidence, the greater the evidence we will require to believe the claim.
So Jeff ultimately defines an “extraordinary” claim as an “implausible” claim. He classifies supernatural claims (e.g. God’s existence, miracles) as “extraordinary” because he views them as implausible.
But, of course, that’s a rigged definition. It begs the question of whether miracles or God’s existence are, in fact, implausible. Yet that’s the very issue in dispute. That’s not something Jeff is entitled to stipulate at the outset.
Only if he already knew that atheism was true or probably true would he be entitled to begin with that presumption. He’s trying to take an illicit intellectual shortcut. Jeff should be fined for trespassing.
I’d also add that there’s nothing philosophically rigorous about calling something “implausible.” That’s hardly a precise definition.