As to the question for why it works, it seems to me that it’s because it takes into account the rationality of each participant (by using the accuracy of their prediction about how many people will agree with them) and then gives the more rational participants’ answers greater weight.
If that’s the case, then any rationality test could be used as a truth serum. If you want to know whether or not string theory is true, you’re probably better off asking people who don’t believe that the Earth is flat.
It’s interesting that the only proposed alternative to Azathoth in this discussion so far is government intervention of one form or another (the government itself is just another creation of Azathoth). But there exist many more such as changing the fundamental institutions of our society, including our very notions of property and democracy.