I am pretty sure that my motivation for this post is simply sufficient annoyance. I admittedly have a rather harsh view of social “science” in general. But this particular study seems to have enough visibility and momentum that I think it’s worth calling attention to a recent rebuttal. Where by “rebuttal” I mean “brutal takedown.”

At issue is a claim by Lu Hong and Scott Page, including empirical evidence from computer simulation and even a mathematical “proof,” that “diversity trumps ability.” The idea is that when comparing performance of groups of agents working together to solve a problem, groups selected randomly from a “diverse” pool of agents of varying ability can perform better than groups comprised solely of the “best” individuals.

“Diversity” is a fun word. It’s a magnet for controversy, particularly when, as in this case, it is conveniently poorly defined. But the notion that diversity might actually *provably* yield better results is certainly tantalizing, and is worth a close look.

Unfortunately, upon such closer inspection, Abigail Thompson in the recent *AMS Notices* shows that not only is the mathematics in the paper incorrect, but even when reasonably corrected, the result is essentially just a tautology, with little if any actual “real world” interpretation or application. And the computer simulation, that ostensibly provides backing empirical evidence, ends up having no relevance to the accompanying mathematical theorem.

The result is that Hong and Page’s central claim enjoys *none* of the rigorous mathematical justification that distinguished it from most of the literature on diversity research in the first place. And this is what annoys me: trying to make an overly simple-to-state claim– that is tenuous to begin with– about incredibly complex human behavior, and dressing it up with impressive-sounding mathematics. Which turns out to be wrong.

**References:**

1. Hong, L. and Page, S., Groups of diverse problem solvers can outperform groups of high-ability problem solvers, *Proc. Nat. Acad. of Sciences*, **101**(46) 2004 [PDF]

2. Thompson, Abigail, Does Diversity Trump Ability? An Example of the Misuse of Mathematics in the Social Sciences, *Notices of the AMS*, **61**(9) 2014, p. 1024-1030 [PDF]

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So you agree with the counterposition and that renders the initial position false and “brutally taken down”? Please. Opinions are an entitlement.

I’m not sure how to respond to this. You seem to be suggesting that it is *I*, and not Thompson, that has “rendered Hong’s position false.” Have you read either the original or the responding papers? If so, can you point out what is “false” in Thompson’s paper? Because there are indeed false claims in Hong and Page’s. Not “opinions” with whom disagreement is perfectly acceptable, but *theorems* whose proofs neglect important (if subtle) assumptions.