Scott Page, an economics, political science, and complex systems professor at Michigan spoke to the ICOS seminar today about his new book The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies.
His talk straddled the line between pop social science books, like Blink or The Wisdom of Crowds, and an academic talk. The line tended to the more pop economics end of things than the academic, but I enjoyed it. He began by reviewing a lot of the material I’ve encountered before in Sami’s prediction market course or Surowecki’s book.
The interesting part came near the end when he introduced some of the theorems he has created to explain the wisdom of crowds. One of them is the Diversity Prediction theorem: Collective Error = Average Individual Error - Prediction Diversity. Diversity in this case is dependent on negative correlation between the predictors in the group.
In the book he describes this as the projection property.
Understanding the Projection Property requires careful thought. It says that if two people look at different attributes of the same perspective (that is, different dimensions), and if the task is to predict success or failure, or any other binary outcome such as good or bad, or yes or no, then when one person is correct, the other person is less likely to be correct. Thus, they’re better at collectively predicting than they’d be if they got independent signals…
The projection property implies that crowds containing people who look at diverse attributes will be wise. Unfortunately, this insight cannot be leverage as much as we might hope. The dimensionality of the perspective defines the number of nonoverlapping projection interpretations. A perspective that creates a five-dimensional representation of an event or situation can support at most five nonoverlapping projection interpretations.
The dimensions he’s talking about here are akin to the criteria used to judge a situation. Page used the example of hiring someone based on charisma or experience in his presentation today. In that case charisma or experience are the dimensions.
I noticed one thing during the presentation that might be an interesting way to look at the problem of gathering collective knowledge. Page mentioned the game show “Who Wants to be a Millionaire?” in his talk, echoing a portion of Surowecki’s book. According to Surowecki, polling the crowd for an answer was correct 95% of the time, and calling a friend (expert in Page’s terminology) was only correct 2⁄3 of the time.
Page and Surowecki assume that the person who was called was an expert. Functionally the ‘call a friend’ was equivalent to consulting an expert. But when I watched the show the contestant was much more likely to call a friend, someone they knew personally and who they guessed might have some information to help answer the question. I think calling these people experts is a stretch.
The real problem with the ‘call a friend’ option is that it in only goes one-degree into the network of people known by the contestant. If there were a way for the contestant to know the skills and knowledge of the people who were two or more degrees beyond her friends then the ‘ask an expert’ possibility would work much more effectively.
And suddenly the problem turns itself into the old knowledge management conundrum of expertise finding. I guess there is some connection in all this information science stuff after all.