take into account that the opinions of other group members may have been caused by swaying rather than independent analysis, but that was already true in the individual accuracy case.
Right, I see. For a group of perfect rationalists, yes, I agree, at least to an extent.
The problem is that this is very hard to do in reality. If I have 15 commenters down/upvote a post or comment I make on LW, how do I know to what extent they're providing 15 distinct opinions vs. 1 opinion followed by 14 swingers? How do I estimate the swinginness coefficient? It seems that group rationality is maximized if individuals state their own opinions on a particular question independently of the group, and only update once a really overwhelming consensus is reached, some time after that particular discussion is over. The group's decision is then the average on n independent opinions. This would make for a very clever group iff each individual is quite clever.
I should emphasize: this will mean that the group (overall) displays smart behavior, but that the individuals do worse than they otherwise would.
Also, how relevant is Robin's paper on Aumann's agreement theorem for wannabe/imperfect bayesians to this debate? It seems that he might (under certain assumptions) have proved the opposite f what I'm claiming here.
Roko, when you run into a case of "group win / individual loss" on epistemic rationality you should consider that a Can't Happen, like violating conservation of momentum or something.
In this case, you need to communicate one kind of information (likelihood ratios) and update on the product of those likelihood ratios, rather than trying to communicate the final belief. But the Can't Happen is a general rule.
Martial arts can be a good training to ensure your personal security, if you assume the worst about your tools and environment. If you expect to find yourself unarmed in a dark alley, or fighting hand to hand in a war, it makes sense. But most people do a lot better at ensuring their personal security by coordinating to live in peaceful societies and neighborhoods; they pay someone else to learn martial arts. Similarly, while "survivalists" plan and train to stay warm, dry, and fed given worst case assumptions about the world around them, most people achieve these goals by participating in a modern economy.
The martial arts metaphor for rationality training seems popular at this website, and most discussions here about how to believe the truth seem to assume an environmental worst case: how to figure out everything for yourself given fixed info and assuming the worst about other folks. In this context, a good rationality test is a publicly-visible personal test, applied to your personal beliefs when you are isolated from others' assistance and info.
I'm much more interested in how we can can join together to believe truth, and it actually seems easier to design institutions which achieve this end than to design institutions to test individual isolated general tendencies to discern truth. For example, with subsidized prediction markets, we can each specialize on the topics where we contribute best, relying on market consensus on all other topics. We don't each need to train to identify and fix each possible kind of bias; each bias can instead have specialists who look for where that bias appears and then correct it.
Perhaps martial-art-style rationality makes sense for isolated survivalist Einsteins forced by humanity's vast stunning cluelessness to single-handedly block the coming robot rampage. But for those of us who respect the opinions of enough others to want to work with them to find truth, it makes more sense to design and field institutions which give each person better incentives to update a common consensus.