I assume the intent is for everyone on the current list to get their turn before the next round begins.
That's what I had been thinking as well.
I had also assumed that each "round" would simply start over with the same list of participants in the same order, but I suppose we could also have everyone "re-up" each time around in whatever order they fall.
I had been running under that assumption, but I think it was decided a couple pages back to just have everyone volunteer for a different order for the next round.
I'm cool with whatever the group decides, I just thought I'd volunteer since NCC-1701