I’m a bit confused by the details of the thought experiment.
When you say “a fictional world where gender wage discrimination doesn’t exist”, that could mean either:
Hiring managers don’t take gender as a direct input on hiring in such a way that the distributions P(pay|gender) = P(hire) if the applicant is equal otherwise. In this case, intervening variables (such as height) might make men paid more than women on average, since they are on average taller and people who are taller are paid more for whatever reason.
Gender doesn’t have any population level effect on pay, i.e. the population distributions P(pay|gender) and P(pay) are equal. In this case, differences between genders that matter for hiring (such as educational attainment) would necessitate that people of different genders be paid different amounts (so that the difference in educational attainment is balanced out by the explicit gender preference in pay).
When you say “negotiate the salary the same way”, it could mean:
Negotiation strategy does not depend on gender (but may depend on, e.g. disposition, in which case we can have intervening variables again)
The people being compared in the thought experiment are forced to employ a fixed negotiation strategy (in which case people with different circumstances or dispositions will apply for different jobs).
It’s the second option in both cases (e.g. P(pay|gender) and P(pay) are equal). In addition, since they do the same work with the same productivity, it’s assumed that they have the same circumstances and dispositions.
I’m a bit confused by the details of the thought experiment.
When you say “a fictional world where gender wage discrimination doesn’t exist”, that could mean either:
Hiring managers don’t take gender as a direct input on hiring in such a way that the distributions P(pay|gender) = P(hire) if the applicant is equal otherwise. In this case, intervening variables (such as height) might make men paid more than women on average, since they are on average taller and people who are taller are paid more for whatever reason.
Gender doesn’t have any population level effect on pay, i.e. the population distributions P(pay|gender) and P(pay) are equal. In this case, differences between genders that matter for hiring (such as educational attainment) would necessitate that people of different genders be paid different amounts (so that the difference in educational attainment is balanced out by the explicit gender preference in pay).
When you say “negotiate the salary the same way”, it could mean:
Negotiation strategy does not depend on gender (but may depend on, e.g. disposition, in which case we can have intervening variables again)
The people being compared in the thought experiment are forced to employ a fixed negotiation strategy (in which case people with different circumstances or dispositions will apply for different jobs).
It’s the second option in both cases (e.g. P(pay|gender) and P(pay) are equal). In addition, since they do the same work with the same productivity, it’s assumed that they have the same circumstances and dispositions.