given that there is little to no correlation between individual rationality and IQ.
There is? On average you would expect individual of IQ 75 to be about as rational as individuals of IQ 140? That seems like a stretch.
In order to plumb the very lowest depths of irrationality, you have to be an intellectual. The low IQ people may go to church and sing and believe vaguely in God and then go home and be no worse off for it, but the most brilliant scholars of the Church invented transubstantiation and decided that the filioque and the apostolic succession would be grounds for religious wars.
This is very true. Smart people can be crazy in ways that less intelligent people would never manage to rationalize. Looking at past and present human societies one begins to appreciate the real downside of the ruling classes tendency to be being above average when it comes to intelligence..
I recommend the book http://www.amazon.com/What-Intelligence-Tests-Miss-Psychology/dp/030012385X on this topic. I don't remember tests measuring aspects of "rationality" were uncorrelated with IQ tests, but they were not highly correlated. Higher IQ people do do better at "rationality" tests when they are prompted with a description of rational behavior, but otherwise they do not do much better.
Per this recent paper, individual IQ has no significant correlation with 'group IQ' (defined and measured as the groups ability to accomplish various tasks); group cohesion, motivation, and satisfaction aren't either. The study identified two things that were positively correlated with group IQ: average social sensitivity and a low variance in the amount of time each person spent speaking. (It also found that having more women improved collective intelligence- because women have better social sensitivity.)
(The remaining stuff is idle speculation from me, not the paper. There's no experimental evidence whatsoever backing it up.)
One possible explanation of the contribution of social sensitivity towards collective intelligence is that it reduces conflicts between group members, allowing the group the remain at least somewhat dispassionate/rational about potential solutions instead of turning discussions about solutions into status pissing contests. This is supported by the fact that ego-based actions are well known to be extremely damaging to group outcomes in sports, and that in contexts (e.g. politics) where there are groups with pre-existing conflicts decision-making seems to be relatively poor despite (presumably) higher social sensitivity on the part of politicians. (This also provides an alternative explanation for the benefits of holding off on proposing solutions: while Eliezer focused, as he is wont to do, on the implications for individual rationality, Maier's edict presumably didn't stop people from thinking of potential solutions and privately settling on a preferred solution- but because they hadn't announced it publicly, they would be more willing to listen to others and change their mind.)
The contribution from variance presumably comes from the fact that if people are on average speaking roughly the same amount, then there are more ideas and perspectives being offered than if only a few people dominated the conversation.
I'd also be interested in seeing whether Collective Intelligence is correlated with individual rationality, given that there is little to no correlation between individual rationality and IQ.