I'm the first author of this paper if anyone has any questions!
This is really neat by the way, thanks for producing this paper, I think it's an important area to start poking around in.
The model predicts that areas in which there is little evidence one way or the other available are the ones where incorrect beliefs could be sustained, particularly when the belief is held by those around you.
I guess one interesting characteristic of certain superstitions is that people will avoid the scenario that they think will lead to a bad outcome, so they actually don't collect personal evidence discrediting that superstition.
This line of argument suggests that positive superstitions should be less persistent than negative superstitions, though I am not sure if that is true.
One mechanism I've heard posited (by Friston's neurosci lab) for how humans deal with noisy environments is to weight our sensory inputs by their expected precision. I might look at the ocean's surface and expect to see a froth of sea-foam, particulate matter, and water, so I won't pay enough attention to see a camouflaged fish. I'll still notice if Godzilla walks up out of it, though.
Would a similar precision-weighting mechanism help to model social trust, and to thus give us an idea of how groups can fixate on incorrect group-beliefs? Are people treating outgroup members or "opponents", so to speak, as uselessly noisy, and thus down-weighting any need to update based on what those persons say or do? Could this contribute to people's (supposed) occasional failures to accurately model their outgroups, since they're intuitively modelling those outgroups precisely as mostly outputting random noise rather than precise information?
It's possible that it's something along the lines you say. Another possibility is people just don't have good estimates of popularity among people they don't know, so they overestimate the popularity of opinions represented in their immediate networks.
Noted in first paragraph: "we still lack a coherent formal perspective on what human collective intelligence actually is". But, why not reference the closest definition or propose your own rigorous definition of collective intelligence to ground assumptions in the paper?
For instance, in 2007 Legg and Hutter presented a paper, "A Definition of Machine Intelligence" (http://arxiv.org/pdf/0712.3329v1.pdf) which inventoried existing definitions of machine intelligence and suggested their own definition. Seems like these definitional papers would be the starting point for presenting research on any kind of intelligence. Do you see meaningful work in this direction regarding defining collection intelligence?
The collective intelligence task in this case is for the community on the site to identify who are the best traders to be mimicking. It's not an explicit group goal, but we are treating it as an implicit one.
I wouldn't say we are trying to define collective intelligence per se. e.g., when you offer a model of a dynamical physical process (maybe a ball arching through the air), you can hardly say that your model provides a definition of that physical system. But you can say that the physical model describes the movement of the ball.
In the same way, I'd instead say we are simply trying to grabble with how to think about collective intelligence.
We are offering a model and a class of models that we expect to display collectively intelligent behavior, and we thereby hypothesize that these models might also explain how collective intelligence in human groups might arise.
After all, a logical statement involves something like X iff Y and Z and Q, so the truth of X might varying discontinuously with average truth values of Y, Z and Q.
You may have one population where 50% think Y, Z and Q are truth and 50% don't and another population where 50% think only Y and Z are truth and 50% think only Z and Q are true. In the first population, 50% think X is true and in the other population 0% think X. But the average truth values of Y, Z and Q would higher in the second population.
I'm kind of shooting in the dark on this one, but Bayesian inference does function as a probabilistic generalization of propositional logic, so in principle it seems like the framework should be able to accommodate at least some kind of scenarios involving logical statements. There are also lots of Bayesian language models.
At the same time, there are impossibility theorems that show beliefs across a group cannot in general be aggregated in coherent ways. (Some of the counter examples look a lot like the one you give.)
So the type of model we are introducing is necessarily only going to be able to apply to certain groups (and perhaps could help characterize collectively rational vs irrational groups).
One other related comment: the case we have dealt with so far is mainly about how groups integrate new information (collective learning), not about the existing prior knowledge knowledge within the group.
Or is it a parallel ... system?