Writing in the wake of this impressive effort by Will Wilkinson can only serve to highlight my own deficiencies, nonetheless there is a point to be made.

Steven Landsburg is by his own standards wrong or at least incomplete when he makes the following claim.

Some people claim (perhaps rightly, perhaps wrongly, perhaps absurdly — I lean toward the latter) that gay people, on average, are less successful as parents. In a video that’s begun to go viral, University of Iowa engineering student Zach Wahls attempts to refute this notion without offering a shred of evidence beyond a single cherry-picked case (his own) to prove that children of gay parents sometimes turn out just fine (except, perhaps, for their ability to reason)

The implicit source of Landsburg’s scorn is that one non-random example should not change people’s estimate of population wide averages. However, this is, of course, false.

If one believes that the “content of one’s character” is a stochastic monotonically increasing function of parenting inputs, then the lower the distribution of parenting inputs the lower the distribution of character contents.

For a very-high-content-character, one far off in the tails of the distribution, a parenting sub-sample that was even slightly below mean could radically reduce the probability of it being produced. A single example of a high-enough content character then should radically lower your estimation of the probability that the parenting sub-sample being tested is below the mean.

Said in slightly plainer terms, a truly exceptional kid would require first exceptional parents and then a heaping of luck on top of that. If gays are actually below average in their parenting abilities then you have to pull a double whammy of drawing first, a pair of exceptional gay parents and then they still have to get a lucky in the parenting business.

Indeed, if homosexuality per se degrades a parent’s ability through the corrosive effects of sin, then it becomes a triple whammy because one has to draw two relatively non-sinful homosexuals – though of course there is presumably significant correlation between mating partners.

Depending on the functions you are dealing with its entirely possible that the appearance of even a single gay couple with a child far enough above the mean would rationally cause one to re-estimate that gays are more likely to be good parents. This, clearly, also depends crucially on priors and assumed distributions.

Now, is this the function we are dealing with? I doubt it because I have seen strong evidence that the parenting to character function is virtually non-existent or more precisely, nearly completely random. But, that’s not the point. Some people believe that the correlation is extremely tight, that the causation runs from parents to child’s character and the distribution of exceptional people is extremely narrow. Landsburg doesn’t offer any evidence that they are wrong.

For Mr Wahl’s monologue to be “intellectual misdirection”, Landsburg would first have to establish that the parenting function or distribution of exceptional character is not of this nature and that further that no one supporting the gay marriage ban believes that it is.

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