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CCC comments on 2012 Survey Results - Less Wrong
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Hmmm. Tricky.
Select a random sampling of people (such as by picking names from the phonebook). Ask each person whether they would like to fill in a survey which asks, among other things, for their IQ. If a sufficiently large, representative sample is taken, the average IQ of the sample is likely to be 100 (confirm if possible). Compare this to the average reported IQ, in order to get an idea of the size of the bias.
Select a random sampling of lesswrongers, and ask them for their IQs. If they all respond, this should cut out the self-selection bias (though the odds are that at least some of them won't respond, putting us back at square one).
It's probably also worth noting that this is a known problem in statistics which is not easy to compensate for.
There's also the selection effect of only getting answers from "people who , when asked, can actually name their IQ".