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.
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?
Yet, even if it were a hammer, getting the nail-like characteristics of an unknown object is very valuable. You just have to repeat the procedure for the other tools on your toolset and you'll either get to completely know it, or characterize a hole on your toolset that can now be filled. A big gain, either way.
Aircraft searches are a big thing, and there's a book on how it has been applied to MH370...
[0] - https://www.amazon.co.uk/Theory-That-Would-Not-Die-ebook/dp/...
[1] Memetics is a theory that the base unit of culture is a "meme" (in the Richard Dawkins sense of shared worldview, not in terms of Pepe. But him too) https://en.wikipedia.org/wiki/Memetics
In the 1970s and 1980s Marvin Minsky developed his "Society of Mind" theory,
based on the idea that human intelligence is the result of a large
society of individually simple (but very different) computational processes
which Minsky calls agents. In his book describing the theory, Minsky sums up
what he sees as the power of this point of view:
Thought it's relevant to mention about it.
The whole premise that people arrive at accurate shared beliefs is rather extraordinary to begin with. In my experience, widely shared beliefs are much more likely to be inaccurate.