My thought is to have three phases or rounds with slightly diff rules. Maybe each lasts for 5 or 7 days.
Round 1: say there are 400 items with 20 users and round 1 is 5 days. 400/20/5 = a limit of 4 items per user per day. But since I only contributed, say 8 items, I don't think I should be able to pick more than 8 items.
Round/phase 2: maybe we increase the daily limit. Am not sure how to handle users who have now picked the number that they contributed.
Round/phase 3: do we say no limit?
Whatever is done, I see a green or red light shown than alerts me that I'm red "met my allowance" or green "limit 4, or whatever, per day" .
Anyway,this is a tough one.
