Given these options, I think I have to reluctantly choose "metaphysically possible."
A decent respect to the opinions of Less Wrong requires that I should declare the causes which impel me to this.
I have never been able to conceive of a zombie and a physically identical non-zombie without subsequently concluding that my conception leads to positing causeless effects (e.g., a zombie spontaneously talking about its nonexistent phenomenal experience while using all and only the cognitive structures that the non-zombie uses to talk about actual phenomenal experience).
But, well... causeless effects aren't incoherent, or metaphysically impossible, they're just vanishingly unlikely. . (Not even necessarily that. E.g., in a world where there are only a few possible utterances, one of which, X, is conventionally understood to be a reference to the speaker's phenomenal experience, it's not even all that unlikely for a zombie to just kind of coincidentally happen to utter X in exactly those circumstances that a non-zombie analog utters them due to phenomenal experience.)
Further, nothing in these definitions asserts that humans do have phenomenal experience, which allows for Dennett's answer ("We're all zombies.") In which case cause and effect aren't even at issue... all of us zombies just happen to talk about phenomenal experience despite not having any, because our brains are wired to do so, presumably for signalling reasons but possibly because the Matrix Lords think it's funny, or for other reasons.
This strikes me as implausible... I mean, it sure does seem to me that I have phenomenal experience, and I can't imagine being wrong about that. But that might just be a failure of my imagination.
Which seems to add up to "zombies are metaphysically possible" on this account.
I'm not quite sure.
How did you answer the physicalism question? If you think any physical duplicate of our world must also be a mental duplicate then I think you're committed to the impossibility of zombies.
Think about it this way: Do you think there can be a world where the distribution of micro-physical properties is identical to ours but which does not have tables? Presumably no, because you believe that once microscopic properties are distributed a certain way in some location, you can't avoid having a table in that location. But you don't think the same is true of pheno...
Despite being (IMO) a philosophy blog, many Less Wrongers tend to disparage mainstream philosophy and emphasize the divergence between our beliefs and theirs. But, how different are we really? My intention with this post is to quantify this difference.
The questions I will post as comments to this article are from the 2009 PhilPapers Survey. If you answer "other" on any of the questions, then please reply to that comment in order to elaborate your answer. Later, I'll post another article comparing the answers I obtain from Less Wrongers with those given by the professional philosophers. This should give us some indication about the differences in belief between Less Wrong and mainstream philosophy.
Glossary
analytic-synthetic distinction, A-theory and B-theory, atheism, compatibilism, consequentialism, contextualism, correspondence theory of truth, deontology, egalitarianism, empiricism, Humeanism, libertarianism, mental content externalism, moral realism, moral motivation internalism and externalism, naturalism, nominalism, Newcomb's problem, physicalism, Platonism, rationalism, relativism, scientific realism, trolley problem, theism, virtue ethics
Note
Thanks pragmatist, for attaching short (mostly accurate) descriptions of the philosophical positions under the poll comments.
Post Script
The polls stopped rendering correctly after the migration to LW 2.0, but the raw data can be found in this repo.