A while back, I posted in the "What are you working on?" thread about a paper I was working on. A few people wanted to see it once I have a complete draft, and I'm of course independently interested in obtaining feedback before I move on with it.
The paper doesn't presuppose much philosophical jargon that isn't easily googleable, I think. Math-wise, you need to be somewhat comfortable with basic conditional probabilities. I'm interested in finding out about any math errors, other non sequiturs, and other flaws in my discussion. I'd also like to find out about general impressions, such as what I should have spilled more or less ink on. Some notation is unfinished (subscripts, singular/plural first person, etc.), but it's thoroughly readable.
ABSTRACT: According to a standard form of the fine-tuning argument, the apparent anthropic fine-tuning of the physical constants and boundary conditions of our universe confirms the multiverse hypothesis. According to the inverse gambler’s fallacy objection, this view is mistaken: although the multiverse hypothesis makes the existence of a life-permitting universe more probable than it would be on a single-universe theory, it does not make it any more probable that our universe should be life-permitting, and thus is not confirmed by our total evidence. We examine recent replies to this objection and conclude that they all fall short, usually due to a shared weakness. We then show how a synthetic reply, obtained by combining independent insights from the literature, can overcome the weakness afflicting its predecessors.
If you'd like a slightly more detailed description before deciding whether or not to read the whole thing, see my post.
EDIT 5/9/12: Current draft (edited, shortened to 13.5K words) is here:
NOTE: The paper occasionally makes use of the notion of a person as a metaphysical individual. Roughly and likely inaccurately, this is the concept of an individual essence that can only be instantiated once in a possible world and is partly independent of the physical pattern it inhabits (i.e. you can have different possible worlds that are physically identical but contain different individuals -- I think this is what Eliezer refers to as "the philosophical notion of indexical identity apart from pattern identity"). I personally find this concept unmotivated to say the least; it figures in the paper only because some of the arguments discussed rely on it; and it is inessential for my proposed reply. If you're going to weight in on this, I'd rather you make suggestions as to how I could gracefully express that I find the concept unhelpful while still engaging with the arguments.