For example, the female's decision to chase could depend on the quality of the male.

I don't remember any of the details, but the fact that "the female's decision to chase" relies on the quality of the male was pretty much how the whole theory worked...

(I am going to quantify/rank people's matability, so that I can make my point quickly. But I do not necessarily think you should do this to actual people, IRL.)

Say Sue is a 6. She will probably be "chased" by 4s and 5s. If she doesn't pursue men herself, then she will date these guys until she finds one that is good enough to not break up with, and end up marrying him.

IF however, she is willing to do the chasing, she will probably chase 7s and 8s (she has 4s and 5s knocking at her door. There is no reason to "chase" them.) Men have had less practice and experience being chased, and are therefore less likely to turn a female down.

Another way of thinking of it (for guys)- There might be girls that you wouldn't bother to pursue, but if she pursued you, you would probably date her.