Can someone explain to me what's wrong with this: If women make $0.70 for every $1.00 a man makes, and women are underrepresented in many lucrative fields, then: an arbitrage opportunity necessarily exists. In other words, if there is systemic sexism, then there exists a profit opportunity for entrepreneurs to buy-up typical companies and replace expensive, scarce male labor with cheaper, less-scarce female labor.
Because pool 1 believes that gender is not a significant factor, they know that wage discrimination on the basis of that factor would be illegal and open them up to lawsuits. Pool 2 does think gender is significant, maybe indirectly laundered through other things like personality assessments, and they therefore think they can and should act on that information.
Critically it doesn’t matter if the sexist pool is openly sexist or using factors more strongly correlated with sex than job performance (like whether or not the employee looks the mental model of the part). The result is the same, they believe they are justified in paying women less. The arbitrage opportunity would never occur to them because they don’t think the labour is worth more.
But if you see the arbitrage opportunity, that puts you in Pool 1 by definition. And so those who are aware of the opportunity know that it would be illegal since the gender isn’t relevant to their position.