It's a co-op games which is meant for playing with a friend/partner, not an MMO....
So if you're friend/partner is too greedy go over to his/her house a slap him/her or just kick him off your session if you are the host....
Just kidding, the "first come first serve" system works quite well in most co-op games I know. Sure, it depends on your co-op partner but my friends and me, we want to have fun in a game and not arguing about loot....
and give myself just what I find is looking nice and lovely (me, playing Scarlett). I don't need te best loot/equipment, I only want the most lovely shiny ones, glittering in the sunlight 
