Today's post, Why Are Individual IQ Differences OK? was originally published on 26 October 2007. A summary (taken from the LW wiki):
People act as though it is perfectly fine and normal for individuals to have differing levels of intelligence, but that it is absolutely horrible for one racial group to be more intelligent than another. Why should the two be considered any differently?
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But that isn't true in general. It might be true under some additional plausible assumptions, but I haven't worked out what those assumptions would be.
The following toy model is a counterexample. Suppose that intelligence is measured by a quantity between 0 and 1. People are paid according to their employer's best guess of their intelligence. (We assume universal employment.) More precisely, the employer computes an expected intelligence E (between 0 and 1) for the employee and then pays that employee at a rate of E utilons-per-hour.
Define "dumb" to mean "intelligence less than 0.5". Define "smart" to mean "intelligence greater than or equal to 0.5". Define "treating a smart person as dumb" to mean "paying an employee at a rate less than 0.5 when that employee's intelligence is greater than or equal to 0.5".
Now consider the following two possible worlds. In both worlds, intelligence is distributed uniformly, in the sense that the proportion of individuals with intelligence between a and b is b − a. World 1 is a world with no observable correlate for intelligence. World 2 is a world that does have an observable correlate for intelligence. I claim that, in both worlds, half the people are paid below their intelligence, but, in World 2 alone, some smart people are treated as dumb.
In World 1, the employer has no information about the employee's intelligence, beyond the uniform prior distribution. This yields an expected intelligence of E = 0.5 for each employee, so everyone is paid exactly 0.5 utilons-per-hour. Thus, in World 1, half the people are paid below their intelligence, but no smart people are treated as dumb.
In World 2, the population is split half-and-half into f-people and g-people. Employers know the actual distribution of intelligence among both sub-populations. An employer can identify an employee as an f-person or a g-person with perfect reliability, but the employer knows nothing else about that employee's intelligence.
The f-people's intelligence satisfies the distribution f, where
Hence, f-people are dumber on average. If I computed correctly, the f-people have expected intelligence E = 5/12. Thus, the f-people are all paid 5/12 by their employers. In particular, some smart f-people are treated as dumb.
Meanwhile, the g-people's intelligence is distributed according to the distribution g, where
Hence, g-people are smarter on average. I compute an expected intelligence of E = 7/12 for the g-people.
If N is the total population size, our assumptions say that there are N/2 f-people and N/2 g-people. I compute that the number of f-people paid below their intelligence is 4N/18. I get that the number of g-people paid below their intelligence is 5N/18. Thus, in World 2, half the people are paid below their intelligence, but some smart people are treated as dumb.
Your scenarios implicitly assume that anyone whose expected intelligence is bellow median will get treated as dumb and that this is somehow much much worse then what happens to people whose expected is exactly median. Furthermore, even under this assumption you will find that your example falls apart if there is any way besides race to obtain information correlated with intelligence.