Page-ing Robin Hanson
By Arnold Kling
I just finished The Difference, by Scott E. Page. I cannot tell whether he has new ideas, or simply weird packaging for ideas that are not very new. He talks so much about prediction markets, sources of cognitive bias, and aggregation properties of voting that it shocked me not to see Caplan or Hanson in the index.From p. 101:
Overall, most experts proved to be more confident than they should have been. Almost everyone suffers from overconfidence.
My favorite line, from p. 117:
Let’s admit that when people…say that “everyone is different, everyone has her own unique set of skills,” many of us would like to barf. Yet the mathematics reveals that those insipid remarks rest on solid foundations.
Perhaps the quote that best sums up the main thesis, from p. 137:
The best problem solvers tend to be similar; therefore, a collection of the best problem solvers performs little better than any one of them individually. A collection of random, but intelligent, problem solvers tends to be diverse. This diversity allows them to be collectively better. Or to put it more provocatively, diversity trumps ability.
Next, we move into Bryan Caplan’s bailiwick. On p. 332:
Empirically, whether we look at cities or countries, we find that the more ethnically diverse groups, the fewer resources devoted to public goods. The pie has to be split too many ways, leading to underprovision of public goods.
On p. 347,
The lack of incentive for voters to develop sophisticated predictive models for electoral decisions creates a fundamental challenge for democracy. Our hope for democracy cannot rest on informed, engaged citizens. It must include diversity as well.
…a society without a diverse economy may lack diverse predictive models. We can even speculate that lack of cognitive diversity might explain the lack of stability in developing countries. A society whose citizens possess fewer predictive models has fewer checks on bad ideas. An effective democracy, therefore, may depend as much on its citizens’ [sic] having diverse predictive models as on their having accurate predictive models, or so says the Diversity Prediction Theorem.
My take on the Diversity Prediction Theorem is that it is a statement that in a regression model if you can find another exogenous variable that is not explained by the variables that you already have, and if the unexplained part is correlated with the dependent variable, then it pays to include the new exogenous variable. That is, of course, well-known mathematically.
The rest is mostly verbal sleight-of-hand. He contrasts expertise and diversity by treating experts as having a set of X variables that are good, but limited and highly correlated with one another. Each non-expert uses X variables that are not as good. However, a diverse set of non-experts collectively uses a set of X variables that spans a larger portion of the prediction space. The optimal prediction would be based on a regression that uses all of the X variables. However, your choice is between two sub-optimal predictions: the prediction of experts, or an average of the prediction of the non-experts. Under plausible assumptions, the latter will be more accurate.
The sleight-of-hand goes further when he connects his mathematical model of diversity to diversity in terms of racial or gender identity. He is very open and cautious when he does this, but it still made me want to barf, to use his phrase.
My guess is that Caplan and Hanson are obligated to read The Difference. I would be curious to see the extent to which they find it enlightening, irritating, or both.