I suppose we can try your way but I see two issues right away.
1. It will be very hard to keep track of who gets next since it's constantly changing.
2. You will probably get only one referral as more people join in, they get to take next one that could have gone back to beginning. Basically as new people join in, they will be on the list right away so unless people stops joining in, you probably only get one and never get referral again
Keeping track should be easy, as people can just work their way down the thread. I agree that as the list gets longer, there will be fewer multiple referrals. As it is though, it seems no one is making past your name (even me!). Is there some point where we'll move beyond the first name?