#Yeah so I have been answering a bunch of threads on how the report system works and I just woke up so.... I realized that this comment was kinda random right after I finished typing it lol. Uhhh yeah... so you can just ignore the text wall if you wanna.
I would assume (don't think the official algorithms have been released for good reason) that reports both add and decay over time, coupled with a strike system.
Lets say the system keeps track of your last 10 games. If you earn a # of reports in those games, say 20 here, then you get a strike. This means that the occasional random report has no real affect on a player. However if you are consistently getting reported, or even just mass reported, you will quickly hit the report limit.
(Note that somewhere it is confirmed that the reports of people who spam report a lot don't count for as much)
Once you hit the report limit you are given a strike, and a punishment. Then your reports would effectively be removed. Every time you get X reports in Y number of games you get another strike, resulting in harsher punishments until you get a permaban.
*Disclaimer: Everything here is based on hints about how the LoL punishment system works and how I would logically go about programming it. The actual way it counts could be very different, but it serves the same general purpose in explanation.