Page, The Difference, part 1

I originally intended to look at Scott E. Page’s book The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies (Princeton University Press, 2007) strictly within the context of my series of posts on crowds. But the book is such a bounteous harvest of insights applicable to the trading and investing world that I decided to take a little more time savoring it. Today I’m going to concentrate on frameworks for modeling diversity--what Page, in a rare accommodation to the trite, refers to as the diverse toolbox.

Page unpacks the notion of diversity, by which he means cognitive differences, into four formal frameworks: perspectives, heuristics, interpretations, and predictive models.

“A perspective is a map from reality to an internal language such that each distinct object, situation, problem, or event gets mapped to a unique word.” (p. 31) For example, we commonly use base ten as a perspective to represent numbers, though it’s only one of many possible perspectives. Or in trigonometry we can represent a point in space using Cartesian coordinates or polar coordinates. Adopting a new perspective can sometimes simplify problem solving. (By the way, one of the delights of Page’s book is his many examples. Since I have no room here to summarize any of them my recap makes the book sound stodgy. It’s actually a lot of fun!) Or, put more formally, “How hard a problem is to solve depends on the perspective used to encode it.” (p. 44)

To demonstrate this claim Page introduces the notion of a rugged landscape. Think of it (and this is my perspective) as akin to an equity curve with local peaks and valleys and a global peak, the point of highest value. “Instead of leading gracefully to a single peak (that looks like Mount Fuji), this perspective creates lots of ups and downs. Moving along it would be like hiking in the Adirondacks.” (p. 45) A rugged landscape perspective isn’t helpful. You get to a local peak and think it’s the global peak; you get stuck. But, Page contends, for any problem Mount Fuji exists; in fact, many Mount Fujis exist. We may not be able to find the perspectives that create Mount Fuji landscapes among the vast multitudes that don’t, but they’re there. (By the way, you don’t have to remind me that we never want equity curves to look like the real Mount Fuji; we want only the left half of the picture.)

Within a given perspective, a heuristic is a rule that tells a person how and where to search for solutions to a problem or what actions to take. For instance, “think like your opponent” or “do the opposite.” It is important to realize that no heuristic works better than any other across all possible problems—the No Free Lunch Theorem. Steven Covey’s popular heuristic “deal with bigger parts of a problem first” may work in some situations, but in other situations it may make sense to do exactly the opposite. Think back to my buttering bread post.

Unlike perspectives that map one-to-one, interpretations lump things together into categories. In a mind-boggling example, Page looks at some dimensions on which people can differ and the number of distinct categories on each dimension.


“The number of different types of people we can distinguish with these categories equals the product of the number of categories: 2*4*10*5*2*4*6*5*5*3*4*2*3. This number exceeds thirty million. Given that a mere three hundred million people live in the United States, this would create one category for every ten people.” (pp. 82-83) Who’d have thunk it? So the pundits rely on big categories, such as soccer moms.

The last framework in the diverse toolbox is predictive models. “A predictive model describes what we think will happen in some context in light of our interpretations.” (p. 90) Predictive models are ubiquitous in our thinking, though on this blog we are particularly interested in “important events such as stock market price changes.” (p. 93) In this context there are two takeaways I want to share from Page’s brief chapter.

First, an example from dog training. “Though lots of noise hinders our ability to predict, adding a little noise has an unexpected effect. It reinforces our beliefs in our models. This has practical consequences. If we want to teach a behavior, a bit of randomness can be helpful. For example, to teach a dog to sit, you should not always give her a treat as reward. Most of the time you should, but every once in a while you should withhold it. In doing so, you make the dog think, ‘I’m sitting, why am I not getting a treat? What is going on here? Didn’t he say sit?’ This helps her brain make even stronger connections between my command/plea to sit and her response.” (pp. 91-92)

Second, in case you didn’t already figure it out, there is no simple way, no Gladwell “blinking” to predict the movement of stock prices. In findings popularized in Moneyball, “more than two hundred studies conducted over the past seventy years demonstrate that simple linear regression models outperform experts in forecasting the future.” (p. 100) These regressions are, of course, based on variables chosen by people—what Page calls interpretations, so the human element is still present. But, he concludes, “Given the diversity of possible interpretations, we have lots of diverse experts. And, as we will see, that’s beneficial.” (p. 101)