# Why statistical discrimination is higher than is either socially optimal or Bayesian rational

Let’s say there is only a mild amount of statistical discrimination in a system. Not prejudice, just a social judgment that some groups are more likely to succeed at some tasks than others. Most people, for instance, do not expect women to reach the NBA, but I would not from that conclude they are prejudiced.

But now introduce a further assumption. There are multiple layers of evaluation, and at each layer people, and institutions, wish to be seen as successful talent spotters, mentors, and coaches. High schools wish to promote students who will get into good colleges. Colleges wish to invest in students who will get into best grad schools, or get the best jobs. Firms wish to hire workers who will rise to CEO, even if elsewhere. And so on. Let’s say there are ten levels to this “game.”

Each level will apply its own “statistical discrimination” tax, whether intentionally or not. Say for instance there is (mild) statistical discrimination against women at the CEO level. Firms that wish to hire and promote future CEOs will be less likely to seek out women to hire, including at lower levels. This may or may not be conscious bias; for instance the firms may decide to look for certain personality traits that, for whatever reason, are harder to find in women. They’ll simply be making decisions that give them plaudits as good talent spotters.

Colleges will then consider similar factors in their decisions. And so will high schools. And so on. In equilibrium, all ten levels of the game will levy a partial “statistical discrimination tax,” with or without conscious bias in thee discriminatory direction.

Does this sound familiar? It is a bit like the double/multiple marginalization dilemma in microeconomics. The number of discrimination taxes multiplies, at each level. Just like the medieval barons put too many tolls on the river. All of a sudden the initially mild statistical discrimination isn’t so mild any more, due to it being applied at so many veto-relevant levels. (As you will recall from the double marginalization problem, each supplier does not take into account the effect of his/her mark-up or tax on the gains from trade elsewhere in the system.)

So say the “Bayesian rational” level of statistical discrimination is a five percent discount. You can get far more than that as the actual effective tax on the disadvantaged group, with everyone in the system behaving in a self-interested manner.

And of course these taxes will discourage effort from the disadvantaged groups, to the detriment of efficiency and also justice.

I am indebted to Anecdotal for a useful query related to this discussion.