It seems to me that that the main effect of your policy will be to introduce a significant selection bias for people who expect general public approval of their views.
More generally, there will be a selection effect for people who want their public persona to include the political views that they express. (Pubic approval is not the only motivation for doing that. Sometimes people seek the sense of solidarity with their co-ideologues that comes from enduring public disapproval.) Plausibly, a large factor determining one's ideological views is the public persona that one wants to craft, for whatever social-status based reasons. Which public personae are most commonly sought by LW users is an interesting question, so I see this selection effect as a feature, not a bug.
ETA: This comment turns out to be irrelevant. I had understood the OP to be saying that our identities would be published with the results, but I was mistaken.
I don't see how the survey is tied to our LW username. I think he just means that he will publish the whole of the data. Yvain's survey didn't even include usernames, it just had karma that might identify specific users. This survey doesn't even have karma.
Some have been curious about what the politics of this community would look like if broken down further; here's a shot at figuring it out. I've also included a few other questions that folks expressed curiosity about. Aside from one sensitive question, there's no option to keep your answers private, since in my opinion that would defeat the point - just don't answer if you have concerns - but there's also no overlap with the old survey, aside from asking you how you answered the original politics question. (This should help with interpreting those results even if the n for this is much lower than and somehow biased relative to the big survey.)
For entertainment purposes only, don't use the below space to discuss politics directly, &c. Early suggestions are likely to be incorporated, given what I assume to be the low quality of the first draft.
Edit: "left" and "right" operationalized for the questions they appear in; poor language cleared up in mental health question.
Edit 2: results here; see comment below for some preliminary thoughts. Because there were several unique regional responses, I did not publish responses that question.