DrCyanide is correct; multiple reports do not stack or do anything different than a single report.
The Instant Feedback System (IFS) will review a player's chat in that game when any number of reports greater than 0 is made against them (for chat offense categories). It will always do this regardless of how many reports, and the review does not work differently depending on how many, so 1 report is the same as 9 reports in a match. You can check Riot Tantrum's post below where he clarified this point (he wrote the IFS); http://boards.na.leagueoflegends.com/en/c/player-behavior-moderation/jmF6VEou-riot-tantram-is-asking-if-the-enemy-is-also-going-to-report-reportable?comment=0003
3 infringements in close succession gets you a chat ban. You don't get banned for flaming one game. Or two. But for three.
I get why you say this, since chat logs will typically show 3 games, but this isn't quite that cut and dry. A chat restriction can (and usually is) an accumulation of many games rather than just 3, you just aren't provided every single game where the system found some negative behavior of yours after a report; it wouldn't be very helpful for the player to be shown games they don't remember or ones that had extremely minor negativity.
A player may also be punished due to fewer than 3 games worth of negative behavior, depending on the severity of their behavior. Someone who has 40 lines of disruptive or abusive chat comms in a single game is probably more likely to be punished for that than someone who has 1 line each over 40 games. And of course, zero tolerance behavior like hate speech can net an escalation to an account ban for a single instance.
I rarely if ever report because this is a competitive game and only when people become really abusive.
That's alright if you don't think another player was problematic for you; if players choose to not report someone's chat, then Riot doesn't have any reason to punish them. However, there are behavior standards in the game which players are expected to abide by, which are basically determined by what Riot and the playerbase at large feels is appropriate for an enjoyable gaming environment. While you don't have to agree with those standards, you still have to abide by them. If you want to chat with your friends in a manner which Riot finds unacceptable, I highly recommend switching to 3rd player comms like any number of VoIP programs available.
And if they tell me to shut up noob I am not going to report them but I am going to call them moronic idiots.
That's not going to help anyone, that just makes people want to avoid you or respond in kind. There has never been a time where that sort of response suddenly made someone untilt and lose tunnel vision.
