@AreYouShiveringI think having any negative system might not be truly representative due to toxicity or frustration. Having a ladder to climb positively though, especially in random matchmaking (due to exploits) could work with badges obtainable like ''till the bitter end'' or ''taking the lead'' to show others you're a team player is potentially a good idea.
Reputation doesn't have to be very obtrusive or giving too much negative feedback to the player. For example, something like this:
Yellow light [neutral]
Red light [negative]l
Green light [positive]
Community Manager
