If I start flipping a coin and half the population guesses heads and half tails and I eliminate the half that guesses wrong, I will eventually wind up with one person with an unprecedented prediction streak.
Yes, but Buffett continued his success for a long time after he'd already been publicly noticed. If you start with a million people, it shouldn't surprise you if someone gets 20 heads in a row- but if they get 30, you need to look for other hypotheses.
The Blue Eyes Puzzle (solution) depicts a paradox: people engage in coordinated action despite having no new information, when "I know you know he knows" reaches a critical mass. Apparently the formal system invented to address this is called Common Knowledge.
Duncan Black complains:
The typical, compelling, explanation for this sort of thing is herd behavior. In the absence of new information, the market is modeled as a random walk, and when the amplitude of its swing happens to get high enough, people see a trend, anticipate it continuing, and thereby create the trend and cause a massive swing.
I wonder if you could instead model stock market swings, or other seemingly unmotivated coordinated activity, as common knowledge reaching critical mass. Say new information was injected into the market two weeks ago, and it took that long to reach a blue eyes catastrophe.
I have no evidence for this other than random pattern matching.