If people agree that the software was correct but that the pairings were poor, there is always the possibility of reevaluating the algorithm itself. For example, an algorithm could be chosen that results in more "mixing."
You can design the algorithm in such a way that your priors are mistaken, or bias creeps in (though theoretically that can be self-corrected). But assuming that's not the case, and the algorithm correctly matches up mostly women v. women and men v. men in a skill parity optimization, you have a fair result for the purpose of a tournemant; i.e. skill-based match-ups.
If at that point you have an issue with the match ups for reasons of gender or ethnic parity, I would argue that you should seek to correct the upstream issues, not the algorithm. In other words, try to get more women playing chess - make the sport appeal to them more, make it more inclusive, etc. Rebalancing an algorithm is, in my view, a handicap, whether it's applied to gender disparity or any other disparity. I feel it does a disservice to both parties and doesn't really solve the root issue.
>I'd like to point out that if you're designing an algorithm to optimize for raw skill comparison in tournament match-ups, optimizing it to rebalance match-up results to be more mixed essentially voids that first optimization
This is not necessarily the case. For example, if you alphabetized by last name, then obviously people with coincidentally the same last name could appear in any order. But if in twenty cases the men always were listed first (that's what the algorithm spat out), it might seem unfair. You could add the first name (another dimension) but you could also add a preference for mixing. Indeed, perhaps adding first names makes it unfair, as the pool of male first names is more skewed toward men (in the way aaron does not have a female equivalent). Last names likely have no such skew since a person born xx or xy gets the same last name.
So this example shows that the first dimension, which is fair (alphabetical by last name) can remain optimized while adding a second dimension. Because the first dimension doesn't care about what order people with the same last name appear.
Likewise perhaps the first dimension is equally fine with a few different pairings - so at that point optimize the second dimension.
For example, if we assumed that the current state had men having twice as many points as women of equivalent skill, it might take a while for people to climb up right?
More generally, it's not like people's skill are well ordered. If so, what would be the point of the tournaments! It seems like having a bit of mixing of levels in the beginning of the tournament would be more interesting. Especially if it's not single elimination