Perfectionism seems like an irrational obsession.  If you are already very close to perfect the marginal benefit from getting a little bit closer is smaller and smaller and, because we are talking about perfection, the marginal cost is getting higher and higher.  An interior solution seems to be indicated.

But this is wrong.  There is a discontinuity at perfection, a discrete jump up in status that can only be realized with literal perfection.  Too see why, consider a competitive diver who performs his dive perfectly.  Suppose that the skill of a diver ranges from 0 to 100, say uniformly distributed, and that only divers of skill greater than 80 can execute a perfect dive.  Then conditional on a perfect dive, observers will estimate his skill to be 90.  But if his dive falls short of perfection, no matter how close to perfection he gets, observers’ estimate of his skill will be bounded above by 80.  That last step to perfection gives him a discontinuous jump upward in esteem.

Now of course in contests like diving, the competitors choose the difficulty of their dives.  This unravels the drive to perfectionism because in fact the observers will figure out that he has chosen a dive that is easy enough for him to perfect.  In equilibrium a diver of skill level q chooses a dive which can be perfected only by divers whose skill is q or larger.  And then the choice of dive will perfectly reveal his skill.  The discontinuity goes away.

But many activities have their level of difficulty given to us, and even among those where we can choose, most activities are not as transparent as diving. At a piano recital you hear only the pieces that the performers have prepared. You know nothing about the pieces they practiced but then shelved.   The fame from pitching perfect game is not closely approximated by the notoriety of the near-perfect game.

You get to see only the blog post I wrote, not the ones that are still on the back burner.

(Drawing: Wait! from www.f1me.net)

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