I answered "psychological", but I should perhaps note that I don't understand "continuing" to imply "uninterrupted". I have no problem with the idea of a personal identity that is shut down for a while before being booted back up (with its internal state saved), or one that is computed on a timesharing system.
Yeah, I should have clarified. "Continuity" here does not mean temporal continuity; it means causal continuity. Future states are appropriately causally related to past states. So if I disintegrate right now, and simultaneously, by some bizarre chance, an atom-for-atom duplicate of me is produced by a thermal fluctuation on Mars, that duplicate would not be me, since the appropriate causal connections between my psychological state and his are lacking.
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.