The way the system works:
need rolls against need (all greed / pass / no-decision treated as pass)
-- If nobody "needs" greed rolls against greed (all pass / no-decision treated as pass)
-- --If nobody "greeds" then all no-decision get a random /roll assigned (pass treated as pass)
-- -- --If EVERYBODY passes then the loot hits the floor.

If you can't obtain the item (you have one / you have left area) it will fall to the next person in line.