The Best Strategy for a "Weak Recruiting" Chapter
So I was thinking about the thread on mutual selection, and who gets to do the selecting, and I said that weak recruiting chapters (hereafter "WRC") don't get to do much selecting. Under RFM, they are heavily recommended not to release too many women.
But then I thought about whether this is really the best strategy, and decided to take a break from my real math work to ponder this.
Let's say that there are 4 chapters, and 100 PNM's, and we can rank both, i.e. the PNM's rank in desirability from 100(best) to 1(worst), and the chapters likewise from 4 to 1. What we'd expect to happen is that PNM's 10076 end up in chapter 4, 7551 end up in 3, 5026 end up in 2, and 251 end up in 1.
Now, let's say chapter 1 is sick of getting the very worst of the PNM's, and they say "forget RFM, we're only going to invite PNM's 100  21 back". Now, there are only 80 PNM's left instead of 100, so PNM's 10081 end up in chapter 4, 8061 end up in 3, 6041 end up in 2, and 4020 end up in 1.
Chapter 1 gets a smaller pledge class, but they have gotten far more desirable PNM's than they would have if they had followed their RFM and invited all 100 PNM's back.
Of course, I have seriously oversimplified the model; assuming there is one round and everyone attends one pref, and then signs a bid card, but it got me thinking about how a WRC could be best off not following the RFM, by underinviting.
I know this ignores retention and everything else, but the basic thing I am getting at is this: If a WRC underinvites, it may be the difference between PNM's having one chapter and no chapters, and therefore being dropped from recruitment altogether. Dropping PNM's obviously decreases quota, but lowering quota usually helps a WRC. So, there is incentive for a WRC to work against what is best for the system.
