From my observations I would say that both men and women are pretty much equal in their fairly indiscriminate mating preferences and the brutal truth is that we're all pretty much fungible when it comes to sex.
I very much enjoy your essays but in this case, I take issue with your assertion that men objectify women as a result of cultural conditioning. Nature objectifies women just as nature objectifies men. The fact that each sex has evolved its own different secondary sexual characteristics is proof of that objectification. The response to those characteristics is innate not learned. And neither sex really needs to know anything personal about a mate in order to copulate and copulate happily with a member of the opposite sex, which again speaks to the reality of 'objectification'.