I was VP Membership in my chapter so I know that picking Littles is almost always a touchy subject. People create friendships with prospective members before Rush and they usually want their friend as their Little. In my chapter we usually ask the prospective members to write down about three actives they would like to have as Bigs (because it is important that Bigs/Littles get along). We take into consideration who the actives want as Littles and who the prospective members want as Bigs. You don't have this problem now, but as your chapter grows you'll need to consider family size and how close each tree is to dying.
I think that it is a good thing to get a Little that you might not know very well. The first time I got a Little I picked one that I really didn't know very well, but I knew that I would get along with. Now we're both very glad things went that way because we are very close friends. We both agree that we probably would not be as close friends if I hadn't picked her.
On the other hand, I have seen girls drop out before initiation because they just could not get along with their Big. So, I don't think that Littles should have just been assigned like that. Maybe you could attend the Exec Board Meeting and discuss it there, before you bring it up in the regular meeting and risk "calling out" you VP Membership in front of the entire group.
I hope this helps you. Good luck!
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