None of the prior discussion reflects an understanding of 'contextualism' as standardly conceived by philosophers (if the Stanford Encyclopedia exposition is representative of philosophers' views). So I suspect the polling data for this question will need to be tossed out. Here's a clearer explanation of the difference between these doctrines:
contextualism = The semantic thesis that 'x knows y' may vary in truth-value depending on the social and psychological status of the knowledge-attributor. I.e., 'x knows y' often or always fails to have a determinate truth-value, unless it is clear from context that we are really saying 'x knows y relative to evaluator z,' where z is someone evaluating 'does x know y?' Thus, a better name for 'contextualism' would be 'attributor contextualism' (which it has indeed been called).
Note that contextualism does not imply that the distribution of knowledge in the world is arbitrary or just a matter of subjective opinion; there may be very strict constraints on what sorts of 'subjective opinions' held by an evaluator affect knowledge-relative-to-an-evaluator. For instance, it is plausible that 'I know I have hands' would count as true if the evaluator were your psychiatrist, but would count as false if the evaluator were someone with whom you were debating the Simulation Hypothesis. That's not because of the evaluator's mere opinions; it's because there are higher standards for knowledge in metaphysical debates than in everyday conversation. An evaluator with crazy, unrealistic standards wouldn't have his/her own, equally legitimate beliefs about what counts as knowledge; s/he would just be consistently in error.
Nor is contextualism a meta-semantic claim about how the word 'knowledge' varies across linguistic communities; rather, it is the semantic claim that 'knowledge' in all (standard-English-speaking) contexts would frequently be judged to vary based on the state of the evaluator. Contextualism could turn out to be false for purely empirical reasons, if, say, sociological data proved that we don't vary in knowledge-attribution based on the mental state and social context of the attributor.
relativism = The metaphysical thesis that knowledge as such is relative to a standard of assessment. Like contextualists, relativists think 'know' is three-place; but their relation is 'x knows y according to standard z,' not 'x knows y relative to evaluator z.' And whereas there are presumably facts about which agent is evaluating a knowledge-claim in the real world, there are no facts about which standard is the 'right' one; so there simply are no facts about knowledge, or even about knowledge-according-to-an-agent. What there are are facts about 'what certain standards treat as being "knowledge"'.
I said that relativism is a 'metaphysical' view, not a semantic one. This is important. Contextualism can be refuted if it turns out that the English language is invariantist; but relativism can't be so easily refuted, since their claim is not that we think of knowledge as relative, but that knowledge really is relative. Relativism is very close to radical skepticism, just with 'knowledge'-talk preserved as a way of signaling one's chosen standards. Whereas contextualism is just as opposed to skepticism as is invariantism. Speaking of which...
invariantism = The claim that we have knowledge of some things, combined with the semantic thesis that contextualism is false and the metaphysical thesis that relativism is false. According to an invariantist, 'I know I have hands' is either true or false simpliciter; evaluators and standards-of-evaluation might disagree about this statement's truth-value, but that's because some evaluators and some standards are wrong, not because 'knowledge' itself is unsaturated.
Source for all this: Rysiew, "Relativism and Contextualism".
In your discussion of contextualism, you are conflating "evaluator" and "attributor", I think. An attributor is someone who makes a knowledge-claim, i.e. attributes knowledge of some proposition to someone (including, possibly, to himself). An evaluator is someone who judges the truth of the knowledge-claim made by the attributor. So if you say "I know I have hands" to a psychologist, you are the attributor, not the psychologist. You are the one making the knowledge-claim (about yourself, in this case). The psychologist is the...
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.