Of course you can optimize for quality and diversity simultaneously. Let's take an extreme example and say that your hiring process only accepts purple people, and then judges them on merit. If you remove the requirement for purple people and keep the rest, your diversity and quality will both improve.

Here's the problem: "Start with some selection of people chosen optimally for job performance...." That's the hiring equivalent of "assume a spherical cow." Sure, if your existing process optimally chooses people for job performance, then any move toward diversity will reduce quality. Likewise, if you have a spherical, frictionless cow, then its speed after descending a slope with a height of 100 meters will be 44.3m/s. Both statements are correct and equally applicable to the real world.

Yea, I thought about that when I was writing my comment, but I wanted a pithy statement, so I omitted the trivial case. How about this: if prioritizing diversity actually changes any hiring decisions made, then it's suboptimal on quality. And if prioritizing diversity doesn't change any hiring decisions, then there's no point to it.

With regards to your second point, this kind of analysis does not require that the employees selected are in fact optimal. It only requires that they're the company's best guess given the inferences from the limited evidence available. Any move away from picking the best guesses will yield choices that are not the best guesses.

Being the best guess given the evidence available implies that the process has no racial or gender bias whatsoever. Which is unlikely. If it does have such bias, then countering that bias will improve the outcome.

To get back to the example of purple people, you wouldn't see a company today which only accepts purple people. However, it's highly likely that people involved in hiring decisions have opinions of purple people, possibly subconsciously, which influences their evaluation of purple and non-purple candidates. If this skews their evaluation toward purple candidates, then pushing things back toward non-purple candidates will give you better results.

This sounds suspiciously like a motte and bailey argument. The motte is that hiring processes have biases so we need to introduce artificial biases to make the process fair. That's quite reasonable (if it's actually true). But what's actually going on in practice is people are unhappy with the gender distribution of the outcome of the hiring process, so they're trying to tweak the process to get equality of outcome. To do so, they're necessarily sacrificing equality of opportunity and simultaneously making bad business decisions by not hiring their estimation of the best according to their interview process.

You're right, hiring in tech has gender bias, but right now that bias leans in women's favor at every step. Other commenters have posted research on this point, but I'll add my anonymous, unverifiable anecdotes to the pile. When I was on hiring committees at my old company, I watched us hire women who performed less well on our technical interviews than men we rejected, for the explicit reason of hiring more women. But I'm savvier than Damore, so I knew when to keep my opinions to myself about it.

And still there's fewer women in tech. There has to be other explanations.

How do you know the process is biased towards women?

As I mentioned earlier, for the company I was part of, that was an explicit goal, and then I watched them hire a less talented woman over a more talented man a couple times. My impression is that this is exactly what diversity initiatives are designed to do.

There are lots of other places in the process which might have bias the other way that you don't see. (And to be fair, they might not, or they might add yet more bias towards women. The point is just that it's really, really hard to evaluate bias from within, or even from without.)