Some months ago I mentioned a textbook called Networks, Crowds, and Markets to Susan Crawford (hat tip for the book recommendation: Nicklas Lundblad). After I told her how the text helps explain the basics about networks, game theory, and more, she said that I had to tell people about the book. So now I am. It is by David Easley and Jon Kleinberg who are both at Cornell. The pre-publication site has the draft text in pdf and the official pub is at Cambridge.
It requires a full read, and I recommend reading it pretty much start to finish. That being said, the sections break out in rather nice ways. For example, the markets and information section offers a great way to understand things that are often thrown around in law and policy circles. The most obvious example is the Wisdom of the Crowds idea. It turns out that only certain types of crowds are “wise.” As the authors point out: “The basic argument there, drawing on a long history of intuition about markets, is that the aggregate behavior of many people, each with limited information, can produce very accurate beliefs.” They explain:
Our results on state prices illustrate some of the technical basis for this intuition. In particular, we found that the crowd at the racetrack determines the odds, or the state prices, and these odds are an average of the opinions in the crowd. If the opinions in the crowd about the probability of horse A winning are independently drawn from a distribution whose mean is equal to the true probability of horse A winning, and if wealth shares are equal, then the state prices actually do converge to the true probabilities as the size of the crowd grows. This occurs because the state prices are actually the average belief in the crowd, and this average converges to the truth with the size of the crowd.
But these claims have two important qualifications embedded in them, both of which are important for understanding the limitations of the wisdom of crowds. First, it is important that the opinions are independent. … Second, it is important that all beliefs are equally weighted.
My read of the above is that those who invoke crowds as being wise should stop and consider whether the judgments are independently made. Online independent judgments are probably not as common as many think. In other words, crowds are not necessarily wise. To be honest, I am not sure I have digested the equally weighted insight. But I defer to the authors about that one.