Unfortunately, I don’t think a blind process would work quite as well for literature. Two cellists, a man and a woman, might audition with the same Bach piece; they won’t be playing their own music. And there seem to be nearly universally agreed upon standards of what constitutes good playing of Bach, which don’t vary much by gender. If they were each playing music of their own composition, we might run into a problem of bias again: namely, that we have been trained to perceive music written by men as great music. You glimpse this thinking in the common question, “Why are there no great female composers?” (Who says there aren’t?)
How Can Literary Magazines Counter Their Biases?