Page, Diversity and Complexity

As long-time readers of this blog know, I’m a big fan of Scott E. Page’s work. Some time back I devoted two posts, imaginatively labeled part 1 and part 2, to The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Society. Page is back with a new book, Diversity and Complexity (Princeton University Press, 2011), that has a more sweeping task even though it is styled as a primer: to elucidate the role of diversity in complex adaptive systems ranging from biological to social (including financial) systems.

One reason that Page is so enjoyable to read, even when he is writing about complicated subjects, is that he has a knack for finding imaginative examples. To illustrate the effects of variation and diversity on complexity, for instance, he conjures up a cakewalk involving nine-year-olds. And, no, it’s not the kind of cakewalk that Debussy’s “Golliwogg” did. To address the sample problem he looks at recipes: “Over what set of recipes do we test whether quality improves with diversity?” If the sample includes all theoretically plausible recipes “diversity does not always increase quality. … Peanut butter-watermelon-squash enchiladas drenched in chocolate sauce doesn’t sound tasty.” (pp. 47-48)

It is difficult to unravel separate threads of this book without doing a disservice to its sophistication and logical rigor. But here’s a topic that is both timely and to me always intriguing—negative and positive feedbacks in systems. “[I]n systems with negative feedbacks, variation produces stability, and in systems with positive feedbacks, variation can make systems more prone to tip.” (p. 160)

As the author writes, “A negative feedback exists when increases in the propensity of an action decrease the benefits from taking that action.” Take the case of 1000 people going to the beach on Saturday. They have a common threshold, let’s say 400, where they all say that the beach is too crowded and they’re not going the following week. If 300 people go to the beach on the first Saturday, all 1000 will go the next Saturday. Oops, too crowded, so no one goes the next week, everyone goes the following week, and the yo-yo effect continues.

Page admits that this is a pretty lame example, but it sets up the problem of maintaining a comfortable temperature in a bee hive. “Bees have an internal mechanism that determines when the hive is too hot or too cold. When it’s too hot, they fan out. When it’s too cool, they huddle together. A hive of genetically identical bees will all get hot and cold at the same temperature.” If, however, there is variance in their temperature thresholds, then as the temperature rises only a few bees will feel the need to fan the hive. “Those few will fan out and reduce the temperature until some of them begin to feel comfortable, at which point those bees will stop fanning and the temperature will equilibrate.” (p. 161)

With positive feedbacks, by contrast, “variation in thresholds leads to an increase in the probability of large events.” Imagine a crowd milling around during a time of social upheaval, with each individual trying to decide whether to riot. “By comparing two scenarios,” Page writes, “I can show how variation leads to big events. In the first, each of one thousand people has a threshold of twenty. Any person who sees at least twenty people rioting will join the riot. The result of this distribution of thresholds will be that no riot occurs. In the second scenario, assume that ten people have threshold zero, ten people have threshold ten, ten have threshold twenty, ten have threshold thirty, and so on. This crowd of people is not nearly as angry as the first crowd. Their average threshold is approximately five hundred. And yet, in this scenario, a riot erupts. This is because, initially, ten people riot (those with threshold zero), and then ten more do, and so on, and so on. The variation in thresholds allows the system to tip.” (p. 162) And, Page continues, makes riots (and, I would add, financial outliers) notoriously difficult to time.

Diversity and Complexity is a fascinating book with obvious ramifications for the financial markets. Read it and you too may come up with some instances of horizontal transfer, which happens “when an idea or solution jumps from one domain to another.” (p. 15)