Cuts, invites, and pref

For pref, if you did not get an invite back from your top 8 houses, then if a house you didn’t rank high invited you back, they would appear on your schedule, this is to maximize your opportunities. For sisterhood it’s 5 house. When you’re getting a house back that you ranked low it’s because houses you ranked high are releasing you. Pref is supposed to be more mutual. You will still rank the 5 houses (if you have that many) and if both of your top 2 houses want you back, you’ll get an invite. If they don’t, it’ll move down your list to the next house that invites you

I’m also a PNM but i’ve heard that the algorithm tends to favor the PNM on pref

Your ranking matters when you have more invitations back than max number of parties you can attend for the current round. For example, going into sisterhood round you can attend a max of 5 houses. If you got invitations from say 6 of the 8 houses you attended at philanthropy, assuming the 2 invites you did not receive were not in your bottom “cut list” then the houses you listed as 1 & 2 of that list would populate into your 5 houses to go to and your 3rd ranked cut would fall off your schedule. Therefore you cut them. As far as pref, if you put a house as your #1 and they put you anywhere within their quota allocation you will get that house. If you put a house #1 and they put you outside of their quota allocation you still have a chance at that house if enough girls within their quota list do not put them first and you can then move up to fall in their quota. The most common way you can end up in your #2 house if the house you ranked #1 does not put you in their quota and your #2 house prioritizes you higher than your #1 house.

The chapters have no idea how you rank them, so your ranks are no influence on their invitations. They decide who to invite back and your ranks only matter if more want to have you back than the max amount per round. Most pnms don't get the max back, and houses will keep showing up because they want you back and the algorithm is trying to give you as full a schedule as possible. This is how pnms don't drop houses, they only rank them.

Pref is a bit different. The algorithm goes down a sorority's ranked bid list and tries to match with the pnms who put them at 1. If necessary to fill quota, the algorithm will make a second pass down the bid list to match with the 2's. The process stops for a sorority whenever they reach quota. If you are high enough on your 1's bid list to match before they reach quota then you will get that bid. If not, the algorithm will try to match you with your 2. If you are not high enough on their bid list to match before they reach quota, you will be a quota addition at either house. This is how you are guaranteed a bid for ranking both houses. The algorithm will try to match you with your 1 as a quota addition, but will also consider your place on both bid lists as well as the number of quota additions to be placed. If you SIP and don't match with that one house, you are out of the process entirely and will not get a bid. If you have only one pref house and you attend and put them on your card you know you are getting that bid.