So the women "Rush" and then how do you as a house find out who wants to join YOU and who doesn't? At that point the first 30 who let you know should be in. If they all descend upon you at once and there are 200 of them, then hold a lottery for the spots. THAT would be fair.
OK, here's how it goes. Now let me say that I went through the process 20 years ago, and I know things have changed just a bit, though not much. I also know that the process is different from university to university, so with that in mind...
In the spring, potential rushees send in their application forms, picture, high school transcripts, and ACT/SAT scores, along with any personal recommendations from adult sorority alumni. The form details the girls personal and academic achievements, honors and awards, hobbies, talents, and interests. Basically a way of introducing themselves to the houses. Each house on campus (for this example, 13), gets a copy and puts it in a book of rushees.
One week before rush, the members move back into the house after summer break, and start preparing for rush, which includes daily study of the rush book, reading all the application forms. Our house used an overhead projector to display the pictures and forms, so we could recognize the girls and become acquainted with their biographies.
First day of rush, each house hosts 13 "parties", where a group of rushees sees the house for the first time, and is taken around and introduced to the members. It is loud and crazy, and hard to truly get to know if the house/rushee is right, but a good introduction. Each rushee goes to a party at each house, and at the end of the evening will fill out a preference form, ranking the houses in the order they liked them the most. The members spend the evening deciding whom to invite back the next day, and a large majority of those not invited back are those who do not meet grade requirements.
Each subsequent day of rush, there are fewer parties (9,7,5,3,2), and during the parties, the members are assigned a certain rushee to escort, so they are able to study the rushee a bit more, and get to know her better. The parties are also longer each day, so there is more time to get to know each other. At the end of each day, the members decide who they want to ask back (based on grades, class in school, and member interaction at the party)as they work their way down to the university quota, issue invitations, and the rushees decide from those invitations where they want to go the next day. If a rushee is invited back to 9 houses on 7 party day, she can cut the two she didn't like, and decline their invitation. After 7 party day, rushees rank the houses who invited them back, so the houses know just how interested they are. In my house, if a rushee ranked us lower than a 3 (or a 3 the night before two party day), we did not ask them back the next day, because we knew they just weren't interested. By two party day, the two houses the rushee visits are both extremely interested in pledging her, and either one would issue her a bid if she ranks them as number 1 on her preference card that evening.
From my experience, each house had a definite "personality", and as the week progressed, I was able to figure out where I felt comfortable, which girls I felt like myself around, and where I could see myself for the next 4 years. When I was in school, it was extremely rare for a girl to not get a bid from a house if she completed rush. Those that did not get bids usually became dissatisfied midway through the process and dropped out, or did not accept a bid because it didn't come from a house they wanted (Many came with pre-conceived ideas of where they wanted to be, and didn't go in with an open mind.). With so many houses, if a girl wanted in a house, there was a place for her somewhere, and the university made sure the pledge class quota reflected that. Yes, girls got cut from houses they really liked. I did, and it upset me at the time, but I found myself in the house where I was meant to be, as did most of my fellow rushees. It was very much a mutual selection process; I got to know them, they got to know me, and in the end we chose each other.