A lot of things get blamed on diversity that may or may not be diversity’s fault, but one thing that is, I think, useful to think about is how a more diverse society can easily be one in which gender identity becomes, as they say, more problematic.

Let’s do a simple simulation. Let’s say there are 10,000 people with chromosomes assigned randomly as either XX or XY. Then, let’s imagine that there is a continuum of gender identity for which XY-assigned individuals are normally distributed with mean 3 and standard deviation 1, and XX-assigned individuals are normally distributed with mean -3 and standard deviation 1, as below:

Of these individuals, roughly 5,000 are XX and 5,000 are XY; roughly 10 will be XY but have a genderscore below 0 (ie, “more female than male”) and roughly 10 will be XX but have a genderscore above 0 (ie, “more male than female.”) So 0.2% of our population is transgender, if you want to call it that.

In addition, if we assume that individuals use as a reference group for gender identity not the “mean” individual with their chromosomes, but the “exemplars” of that identity, we could ask how far an average individual thinks of themselves from those exemplars. That is, the mean individual with XY chromosomes has a score of 3, but the 90th percentile XY score is 4.3, and the 99th percentile XY score is 5.3. So, an “average” XY considers themselves 1.3 away from a “top tenth” masculinity XY, and 2.3 away from a “top percent” masculinity XY.

Now, let’s change the simulation. There are now three groups: A, B, and C. The 30% of the population in group A have a genderscore is shifted 1 unit to the right: XY individuals in group A are distributed normally around a mean of 4, and XX individuals in group A are distributed normally around a mean of -2. The 30% of the population in group C have a genderscore shifted 1 unit to the left: XY individuals in group C are distributed normally around a mean of 2, and XX individuals in group C are distributed normally around a mean of -4. Now this is what the population histogram looks like:

Not that different overall, but now about 30 individuals are XY but have a genderscore of <0, and about 30 individuals are XX but have a genderscore of >0; 0.6% of our population is transgender, according to our earlier definition.

In terms of reference groups, while the mean across everyone is still 0, and the mean for XX is still -3, the average XX is now 1.65 rather than 1.3 from a 90th percentile femininity XX, and 3 rather than 2.3 from a 99th percentile femininity XX. Moreover, an XX individual in group A is now on average 1 points from the mean XX, 2.65 from the 90th percentile XX, and 4 from a 99th percentile XX.

Do I think that this is “really” how gender works, or how transgender identity originates? No, it’s a stupid 10-line Stata program. But I do think it’s suggestive of how, aside from the cultural changes that effectively narrow the scope of gender identity for most individuals even as “officially sanctioned” alternatives are opened, the tendency is towards an increasing experience of failing to live up to gender roles, both as society becomes more diverse, as sexuality becomes the sole marker of adult identity, and as people’s reference group is formed out of mass media images- which tend to select from extremes- rather than their family or an immediate community composed of people more-or-less like them. (Feminists may say they’re trying to strike down limiting portrayals of femininity, but 13 out of 13 girls in my son’s kindergarten class last year listed “Frozen” as their favorite movie on the beginning of the year “all about me” questionnaire.)

As Scott Aaronson said, he was “shtetl-optimized,” but he’s not in the shtetl anymore.