I know Tufts University has a "generally assured bidding" policy where if I women does all the things she is supposed to do in rush (like goes to all the parties and stuff) but is cut by all 3 houses then she automatically gets invited back to all 3.
For pref if she got cut again she would get invited back to all 3 and choose the 2 she wants for pref.
If she still doesn't match the advisors sit around at bid matching and discuss (ok argue) about where she will be placed. A lot of time the sorority that released her last (ie if two house cut her after open house but one kept her) gets her.
It is a univeristy imposed rule and there is no way to change it
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