The Best Strategy for a "Weak Recruiting" Chapter

[DeltaBetaBaby]

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 100-76 end up in chapter 4, 75-51 end up in 3, 50-26 end up in 2, and 25-1 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 100-81 end up in chapter 4, 80-61 end up in 3, 60-41 end up in 2, and 40-20 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 over-simplified 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 under-inviting.

I know this ignores retention and everything else, but the basic thing I am getting at is this: If a WRC under-invites, 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.