[CarolinaCutie]

Originally posted by DeltaBetaBaby
It really doesn't affect the first round of invites, only later rounds. Let me see if I can explain why...

Let's say we can rank all PNM's on a campus from 1 - 10, with an equal number of girls in each group. Let's also say that we can clearly rank the ten chapters on her campus from 1 - 10.

(note that these are terrible assumptions, because different chapters offer different things, and look for different things in PNM's, but I do math for a living so I like to put everything into numbers)

Suzie PNM is a 6, so 50% of PNM's are more desireable, 10% are the same, and 40% are less desireable. After round 1, Suzie gets invited to all ten houses, because even the biggest chapters are allowed to invite 70% of the PNM's back. She picks chapters 1, 2, 3, 4, and 5, dropping 6 through 10. So does every other girl in the top 70%.

Now, in the view of houses 1 through 5, Suzie is more desireable than only 14% of the PNM's left in their pool, equal to 14%, and less desireable than 72%. If they are again allowed to invite back 70% of the PNM's, OOPS, Suzie has no invites.

Let's replay this with top chapters only being able to invite back 50% of girls, and smaller chapters being able to invite back 100%. Suzie gets invites to 6, 7, 8, 9, and 10, and goes back to each of them. The same goes for all the girls in the lower 50% of the PNM pool.

Now, in the view of houses 6 through 10, Suzie is in the top 20% of PNM's. She will get five invites back to the next round.

The girls in the top 50% are unaffected by this change, as are the girls in the bottom 30%, but the 20% that would have been invited to chapters 1-5 in the first scenario but not the second are much more likely to find a home.

You are my math hero Thanks for that!