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On the invisibility of the given

February 9, 2010

In my posts on the free market, I have really harped on the idea that we tend to forget what aspects of society are “given,” and which parts of society are, in some sense, in flux. Admittedly, my thinking on this has followed from my training in probability. Probability provides us with the symbols to express this distinction between the given and the uncertain with elegance.

For example, let Y be a random variable representing a household’s annual income. E( ) is the “expectations” operator, which most people know as the mean or average. So we read E(Y) as “the expected value of Y,” or “the average household income.”

E(Y) = 50,000

We can also read this as, “If we didn’t know anything about you, our best guess would be that your household makes $50,000.” But if we do know something about you, then we want to factor this into our estimate. The vertical bar “|” is inserted in the argument of E( ) such that everything to the right of the bar is given, and everything to the left of the bar is uncertain (i.e. subject to probabilistic forces). On the right, we put the conditions of our query. On the left, we put the unknown value that we want to determine, after having “controlled” for the given, and for the probabilistic forces.

So we read the expression

E(Y|Black) = 30,000

as “the average household income, given that you are black, is $30,000,” while we read

E(Y|White) = 55,000

as “the average household income, if all we know is that you are white, is $55,000.”

On the one hand, this statistical shorthand is perfectly intelligible. We all know what I mean by “given that you are black, your expected income is $30,000.” But from another perspective, this notation is pure nonsense. “Blackness” is not some elemental force. It’s just the state of having black skin, and because black skin does not exert any elemental forces, it has no intrinsic effect on income. In short, there is no eternally applicable law of skin color and income waiting to be deduced from intercourse with pure logic.

Strictly speaking, then, we are never conditioning on black skin alone. Implicit in our model is everything else that we are taking for granted. If we were to fill out our models more fully, they would read:

E(Y|The fact that your skin is black, and the fact that you live in a country with a racial history of … and … , and where race still matters because of … and …)

Why don’t we write this all out? Probably because we don’t have many relevant counterfactuals. Between the legacy of colonialism and the ubiquity of modern media, I wouldn’t know where to collect data to evaluate the statement:

E (Y|The fact that your skin is black, and the fact that you live in a country where race never mattered)

Of course, we could extend the “given” side of the model ad absurdum. Why not mention that we are assuming the laws of relativity and the mass of the sun? The point is that while shorthand like race is convenient, we should always keep in mind that we are conditioning on easily observed characteristics that mediate deeper social processes. We only rarely condition on the ultimate causes themselves. Black skin, in and of itself, has never been the cause of anything.

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From → Methodology

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