In today's depressing news from the Harvard Business Review, if there's only one woman or racial minority candidate in your hiring pool, statistically, you will never hire her. hbr.org/2016/04/if-the…
A bunch of this research was done, incidentally, on finalist pools, not just hiring pools. So the hypothetical female candidate here isn't a random candidate. She's one who's made it into the final short list.
Combine that with this equally depressing article, also from the Harvard Business Review, about how women must outperform men in order to be evaluated as equal to male peers. hbr.org/2017/10/resear…
So, in the initial pool of candidates--everyone who responds to a job posting, with no filtering, you have wildly varying levels of quality/qualifications. If there's a woman in that pool, it says nothing about her level of qualification--only her interest.
But with your finalist group, presumably you've reduced the variance in quality considerably--you've advanced only the most qualified to the final short list.
What the actual DATA here says is pretty clear: unless the process up until this point has been blind, you should probably just hire the woman, because for you to judge her as equal to her male peers, she actually has to have outperformed them.
But HBR's research says that unless there are multiple women on that shortlist, there's a 0% chance that you hire her, despite bounteous research also saying that if she looks (to you) comparable to her male peers, she actually outperforms them.
However, there is a glimmer of optimism here: as soon as you add a second female or minority candidate to the pool, the odds that you'll hire a female or minority candidate increase significantly. And statistically, there's no good reason for NOT having more than one. 
It's not unfair preference, it's not giving less qualified applicants a chance for "diversity" -- the data shows that if you *didn't* know their race or gender, you'd be picking the female/minority candidates.
