I've been wondering whether the non-contingency of moral realism (it's either true in all possible worlds, or false in all possible worlds) undermines parsimony-based objections to it.
We can explain all our observations without appeal to moral facts. So, the argument goes, that's precisely what we should do -- why multiply entities beyond necessity? Of course, I'm inclined to start with a broader conception of the philosophical data to be explained, but parsimony is surely worth something, and it isn't difficult to get into a skeptical mindset of wondering whether the theoretical "costs" of positing moral properties shouldn't lead us to instead take anti-realism as the "default" position.
But now notice that in the standard cases (teacups orbiting Pluto, etc.), we don't take the more complex hypothesis to be impossible or anything, but merely less likely to be actual. So, we might interpret the basic rule of parsimony as follows: given a set of possibilities, distribute your credences (all else equal) in proportion to the simplicity of each hypothesis.
The precise details don't matter here. What's interesting about this interpretation of parsimony is that it would render the principle entirely inapplicable to the moral realism debate. For there we are not "given" rival possibilities, either of which might (with greater or lesser likelihood) turn out to be actual. Rather, the debate is about what's true of the possibilities themselves -- e.g., is any possible instance of gratuitous torture non-instrumentally bad? Is fine-grained description D a case where moral property M holds? These questions don't hang on the contingencies of what happens to be actual. So, if parsimony only speaks to the latter, then it just doesn't have anything to say about the former questions.
Which is, perhaps, all just to say that moral anti-realism is a stronger position than it might at first appear. It's not just to claim that there happen not to be any moral properties. Really, the anti-realist is committed to the stronger claim that there couldn't be such properties. But why should we think that? Mere parsimony doesn't seem to establish impossibilities. So it seems that the real case against Moral Realism must rest on other grounds -- arguments that attack, not its likelihood, but its very coherence. (E.g. Humean worries about "necessary connections" and the supervenience of the normative upon the non-normative; or perhaps confused worries about how non-natural properties could be normative at all.)