The Inverted U-Shaped Curve

Does more always mean better?  If devoting resource x to a social undertaking is good, shouldn’t x+1 be better?  And x+2 better still?

Not necessarily, argues Malcolm Gladwell in this talk at Microsoft regarding inverted U-shaped curves.

Humans intuitively visualize a linear-shaped model, where the more we input toward a desired outcome, the better.  In some cases, the slope may flatten the further you go (diminishing marginal returns), but it’s still going upward.

But with an inverted U-shaped curve, there is a point where the slope starts pointing downward.  In other words, allocating more resources toward a problem not only ceases to be helpful, it actually makes outcomes worse.

Gladwell elaborates on two examples to illustrate this phenomenon: school class size and imprisonment.

There’s a general public consensus that students learn better in smaller classes–and to some extent, they do.  But, according to Gladwell, when classes get smaller than 20 or so students, the benefit disappears.  A couple theories as to why are that class discussions suffer with fewer participants, and student peer support declines when there are too classmates.

The model is even more counter-intuitive when it comes to crime and punishment.  Isn’t society always better when it keeps criminals locked up?  Perhaps not, if you imprison too many people for too long.  The problem is that although they may not be great role models, prisoners often have dependents.  And if you remove too many fathers from their children, it can be detrimental to the community, perpetuating the cycle of crime.  Moreover, people are much less likely to commit crime once they reach their 40s.  So long sentences for some crimes–e.g., drug offenses–are an increasingly inefficient allocation of resources over time.

Gladwell cites a few more examples of this in the Q&A session–e.g., wealth and happiness. In fact, he goes so far as to state that it’s difficult to think of a case where the linear model is more useful than the U-shaped model.

What do we take from this?   That often there can be too much of a good thing.  We need to systematically monitor outcomes to ensure resources are being used efficiently.  And lastly, there’s wisdom in the adage: “Everything in moderation.”

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