Ah, I get it now
When I joined my local, bigs and littles were matched up right after rush! 5 out of 7 sisters were eligible for littles, and there were 5 new members, so we just ranked the sisters 1-5 and they matched us up.
From then on, new members were given a list of eligible sisters and asked to rank their top 3 choices. The new member educator then matched them up. The NM educator was ineligible to have a little, and you were ineligible if you'd gotten a little the previous semester. Attempts were made to ensure that all sisters had the opportunity to have at least one little unless they were totally uninterested.