The Wisdom of Crowds, The Madness of Crowds, and Brownian Motion
Friday, March 28th, 2008Two of my favorite books are James Surowiecki’s The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations and Charles Mackay’s Extraordinary Popular Delusions and the Madness of Crowds (fun fact: MacKay’s book, when originally published in 1841, was Extraordinary Popular Delusions and the Madness of Krauts. Apparently, this title fell out of favor at some point). Surowiecki’s work argues that the collective wisdom of groups is superior to the knowledge of any individual in that group. Mackay tome instead chronicles the frequent instances in history in which the crowd has practiced a sort of collective insanity (frequently in the form of some sort of bubble). So, which is it: are crowds wise or crazy?
There are many people smarter than I that are thinking about this apparent paradox (including Surowiecki himself), so I won’t claim to add anything substantive to the debate. However, I think there are some really interesting analogies to be made to Ben and my own chosen field of chemical engineering. According to Surowiecki, four elements are required to form a wise crowd: diversity of opinion, independence of opinion, decentralization (people can draw on local knowledge), and aggregation (some mechanism to collect this knowledge). From an engineering perspective, those four qualities are the same four qualities of an ideal gas - basically, a dilute mixture of gas molecules moving about via random Brownian motion. Although the molecules of an ideal gas move about randomly (independence and diversity of opinion), collectively, they move so as to maximize the entropy of the system (aggregation). And, from information theory, entropy=information, so that in maximizing entropy, the gas molecules (or, in our case, investors), are maximizing the information content of the system. Although no individual gas molecule knows anything about the entropy, collectively they maximize it. Sounds like the efficient market hypothesis, no?
So, if the wise crowd is a container of ideal gas particles, when does the crowd go mad? In keeping with our analogy, the crowd goes mad when someone turns on a fan. Now, all our gas molecules are moving in one direction, and brownian motion is overwhelmed by convection. Maybe the fan is the media, a new investment product, a new technology, or something. But when we turn on the fan, all bets are off.
End nerd talk.