The Likelihood Ratio and the Problem of Evil

Are you hoping someone will explain why your point is obscured, or do you want an explanation of how your math is bad? I assume the latter, so I'll try to point out a couple of places where your math goes wrong (really just re-iterating stuff that has already been said, but hopefully in a clearer way). Apologies if I'm misinterpreting your question. Here are some of the more obvious errors in your analysis (not all mathematical):

1. H and ~H are not merely mutually exclusive, they are also exhaustive. Every possible state of the world must be compatible with either H or ~H. Intuitively, if a hypothesis H picks out a certain set of possible worlds (such as the ones with an all powerful creator god), then ~H must be true in all other possible worlds. You seem to choose H and ~H (and later in your article E and ~E) to be two exclusive hypotheses without bothering about them exhausting all possibilities. "Universe created by an all-powerful god" and "Naturalism" do not exhaust the space of hypotheses. There are possible worlds that are neither created by an omnipotent deity nor naturalistic.

2. Your rationale for assigning a high value to Pr(Our universe | Naturalism) is weak. You say that naturalism postulates a fundamentally uncaring universe. OK, but why does this entail that we should expect a naturalistic universe to contain the precise mix of good and evil we see? I would think that the hypothesis of an uncaring universe should lead us to think that no particular ratio of good and evil is more favored than any other. So, conditional on the naturalism hypothesis, we should have a uniform distribution over various ratios of good and evil. But this is precisely the sort of distribution you attribute to the theist position -- a distribution that doesn't restrict anticipation -- so I don't see the advantage for naturalism. Of course, all of this assumes that we can make precise sense of the good:evil ratio in a world in the first place (see shminux's comment).

3. I doubt that any moderately sophisticated defender of the fine-tuning argument would concede that the god hypothesis could equally account for any set of physical constants. The whole point of the argument is that the fine tuning of the constants makes the god hypothesis more likely. If they have even a modicum of knowledge of Bayesianism (and I'm sure some of them do), proponents of this argument would recognize that it follows that there must be certain possible ways the universe could be (not conducive to life, perhaps) that would make the god hypothesis less likely. I actually tend to agree that the fine-tuning of the constants is some evidence for the existence of god, but given the miniscule prior probability of the hypothesis, it's not nearly enough evidence to make the hypothesis worthy of serious consideration.

4. How does the hypothesis of naturalism restrict anticipation when it comes to the fundamental physical constants? Is there any value of those constants that is ruled out by naturalism? Is there any value of those constants that is more likely than any other value given naturalism, assuming equal priors?

5. At the end, you say that any hypothesis that fails to restrict anticipation over an infinite sample space must be infinitely less likely than a hypothesis that restricts anticipation over the same sample space. This is wrong. A Gaussian distribution over some continuous sample space restricts anticipation, and a uniform distribution doesn't. It is, however, not the case for any piece of evidence from this space that the likelihood of the Gaussian hypothesis is infinitely greater than that of the uniform hypothesis. Perhaps you intended to talk about an unbounded sample space rather than just an infinite one, but there is no such thing as a probability distribution over an unbounded sample space that does not restrict anticipation. You can't have a uniform probability distribution over all the real numbers, for instance, because there is no way that such a distribution could be normalized.