The people who take the survey know that their IQ contribution is going to be watered down by the 1000 other people taking the survey.
I have thought of that. But a person who wants to lie about his IQ would think this way: If I lie and other LWers do not, it is true that my impact on the average calculated IQ will be negligible, but at least it will not be negative; but if I lie and most other LWers also lie, then the collective upward bias will lead to a very positive result which would portray me in a good light when I associate myself with other LWers. So there is really no incentive to not lie.
(I'm not saying that they definitely lied; I'm merely pointing out that this is something to think about.)
How likely is it, do you think, that this group of rationality-loving people has reasoned that claiming to have joined a group that anybody can join is a good way to brag about their awesomeness?
Fair point; but very often the kind of clubs you join does indicate something about your personality and interests, regardless of whether you are actually an active/contributing member or not. Saying "I read LessWrong" or "I joined LessWrong" certainly signals to me that you are more intelligent than someone who joined, say, Justin Bieber's fan club, or the Twilight fan-fiction club. And if there are numbers showing that LW readers tend to have IQs in the gifted range, naturally I would think that X is probably quite intelligent just by virtue of the fact that X reads LW.
One last point is that LWers might not be deliberately lying: Perhaps they were merely victim to the Dunning-Kruger effect when self-reporting IQs. I am not sure if there are any studies showing that intelligent people are generally less likely to fall prey to the Dunning-Kruger effect.
Last but not least, I would again like to suggest that future surveys include questions asking people how much time they spent on average preparing for exams such as the SAT and the ACT -- as I pointed out previously, scores on such exams can be very significantly improved just by studying hard, whereas tests like iqtest.dk actually measure your native intelligence.
That most people lied about their IQ, and fudged their SAT, ACT and personality type data to match, or that they're telling the truth?
Scores on standardized tests like SAT and ACT can be improved via hard work and lots of practice -- there are abundant practice books out there for such tests. It is entirely conceivable that those self-reported IQs were generated via comparing scores on these standardized tests against IQ-conversion charts. I.e., with very hard work, the apparent IQs are in the 130+ range according to these standardised tests; but when it comes to tests that measure your native intelligence (e.g., iqtest.dk), the scores are significantly lower. In future years, it would be advisable for the questionnaire to ask participants how much time they spent in total to prepare for tests such as SAT and ACT -- and even then you might not get honest answers. That brings me to the point of lying...
it's not like the liars are likely to get anything out of boasting anonymously
Not necessarily true. If the survey results show that LWers generally have IQs in the gifted range, then it allows LWers to signal their intelligence to others just by identifying themselves as LWers. People would assume that you probably have an IQ in the gifted range if you tell them that you read LW. In this case, everyone has an incentive to fudge the numbers.
erratio has also pointed out that participants might have answered those personality tests untruthfully in order to signal intelligence, so I shan't belabour the point here.
Clarity cannot be over-valued; plausibility, however, can be under-valued.