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Great explanation, AZ-AlphaXi.
It's worth noting that under either system (priority rank vs. accept/regret) a PNM could still end up being forced to go back to a sorority she doesn't like. Say there are 8 sororities, and a PNM comes out of round 1 hating two of them. She gets 7 invitations to round 2, including both of the sororities she dislikes. She can go back to 6 sororities. Usually, if you get more invitations than you can accept, you must decline down to the max # you can accept, but you can't decline any other invitations - you have to end up with a full schedule. So the PNM can decline the invitation from one of the 2 sororities she dislikes, but she'd have to keep the other.
Or, the PNM might receive only five invitations, including the two sororities she dislikes. She would then have to go back to all 5 if she wants to stay in recruitment.
Of course, in taking a second look at sororities she didn't like after round 1, the PNM may find she does like them after all.
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