The Racialists are Right. Again.

by David Sims

THE SMUG “Debunking Denialism” Web site, which likes to style itself as scientific and rational, says that “racists” employ fallacies in their arguments:

Thinking that the average says anything about the spread [is a fallacy]. This fallacy can often by found in racist or anti-immigration rhetoric. It is the fallacy of claiming that the average (say, intelligence or prevalence of crime) is different a particular group A compared with another group B, therefore, it is reasonable to treat individuals in group A as if they, say, had lower intelligence or higher prevalence of crime. This is an erroneous argument, because the average says nothing about the spread, that is, how different individuals in the group are distributed. When it comes to IQ scores, a group A in which individuals all have precisely 120 IQ will have a higher average IQ than a group B in which half of the individuals have 95 IQ and the other half 140 IQ (0.5*95+0.5*140 = 117.5), yet clearly half of the individuals in group B have a much higher IQ than individuals in group A, despite the fact that group B containing individuals with a lower IQ than individuals in group A. This could feed into a stereotype of thinking that individuals in group B have less IQ than those in A. These groups and figures are just made up for the purpose of a simple explanation and does not refer to any actually existing group.

I’m going to take issue with that claim.

“Racist” and anti-immigration rhetoric is seldom so simplistic and fallacious as the author of the article says it is. Rather, it takes the spread of the data into account in a comprehensive way.

The broad character of the spread of human intelligence (or in the tendency to commit crimes) is that of a normal (Gaussian) distribution, or a bell curve. Many human physical and behavioral traits are largely inherited as a potential maximum (or minimum), with environmental factors conditioning the extent to which the potential is realized in the individual. A person born with an inherited potential for reaching an adult height of six feet might, because of poor nutrition during youth, only grow to 5’10”. A person born with a genetic potential to have an IQ of 130 might, for the same reason, only reach IQ 120. But no environmental factor can lift an individual above his inherited potential; indeed, trying to do so is simply a waste of resources.

The normal distribution of inherited traits is a result of how biological inheritance works, provided the trait in question is the result of more than one allele in the individual’s DNA. (Think of tossing dice and recording the totals of upward facing dots.)

The significance of distribution differences between races for IQ has to do with the utility and cost-effectiveness of the racial populations. How much “bang for the buck” (e.g., economic productivity per calorie consumed) do you get from Race A, as compared with Race B? How do the cost-benefit ratios of different races compare with each other?

The fraction, f, of a race having an average IQ of x̄ and a standard deviation in IQ of σ, which is above the minimum IQ of μ.

f(μ) = [σ√(2π)]⁻¹ ∫(μ,∞) exp{ −[(x−x̄)/σ]²/2 } dx

Taking advantage of the normal distribution’s symmetry, we make it more easily integrable.

f(μ) = ½ − [σ√(2π)]⁻¹ ∫(x̄,μ) exp{ −[(x−x̄)/σ]²/2 } dx

You can avoid integrating the probability density function if you have a handy error function to call.

f(μ; x̄, σ) = 1 − ½ { 1 + erf [(μ−x̄)/(σ√2)] }

For the White race,
x̄ = 102
σ = 15

For the Black race [in the US],
x̄ = 85
σ = 13

Let us suppose that an employer is hiring for a job that, in the employer’s opinion, requires a minimum IQ of 130 for satisfactory performance. His business is located in a demographically average part of the United States, where Whites outnumber Blacks by a ratio of five to one. Suppose, further, that both Whites and Blacks in the area are unemployed at the same rates and without regard to their IQs (i.e., the unemployed Whites have the same IQ distribution as the employed Whites do, and likewise for Blacks).

What fraction of the unemployed Whites is qualified, by reason of IQ, to be hired for the job? What fraction of unemployed Blacks is similarly qualified?

f(130; 102, 15) = 0.030974076
f(130; 85, 13) = 0.000268549

We would expect, therefore, that the employer would hire 577 times as many Whites as Blacks for his job openings, if he were to exercise no racial bias whatsoever.

That’s the “racist” argument: that jobs demanding intellectual skills will be filled by Whites (or by Asians), nearly to the exclusion of Blacks, when hiring is done based on intellectual qualifications alone, i.e., in the complete absence of “racist discrimination.”

Suddenly, the “racist” argument doesn’t seem nearly so facile as the writer of the linked article put it.

I’ll anticipate a leftist come-back argument. They’ll say (depend on it) that we should treat everyone as an individual, and that, for example, Blacks who are sufficiently high-functioning and compatible with Whites should be included in every kind of endeavor by Whites.

But that is not the case at all. For one thing, just because a particular Black is intelligent and well-behaved does not mean that his children, grandchildren, great-grandchildren, etc., will be equally worthy.

In every race, the laws of genetics make a regression to the racial mean the most probable result of biological inheritance. The descendants of any exceptionally worthwhile subset of Race A will be more typical specimens of Race A than their cherry-picked ancestors were. And that means individual worthiness does not make it reasonable to make exceptions to a policy of racial exclusion of Race A from the territory of Race B.

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Joe Lowsac
Joe Lowsac
22 May, 2022 7:30 am

That the average tells us something about the spread is not a fallacy. An average indicates the middle of a scale of evaluation. This is true even in the ridiculous example given. The average tells us 117.5 is the middle of the spread in group B and that the average of the test scores in group B were 2.5 points below those in group A. That’s not much but it’s considerably more than nothing. I did identify a number of logical fallacies in the argument however (not counting the inaccurate fallacy claim). 1) False Analogy 2) Argumentum Ad Consequentian 3) Dicto Simpliciter 4) Vacuous Truth Some people may not like the fact that the average of 140 and 95 can’t ever be higher than an average of 120, it may… Read more »