Limit the amount of reports and honors, and make them mean something.
It's just like inflation.
At the moment both honors and reports aren't worth ANYTHING. I report people. People say they will report me. I honor someone. They honor me. Guess what happens? Nothing. Unless this kid literally goes 0/20 and said the N-word 3 times, I've never seen anything done about reports.
I recommend doing it Dota 2 style, where you get ~6 honors and reports per week. That way people aren't throwing out reports at people for "feeding" when they go 3/7. They'll actually have to use their reports wisely one people they legit think should get punishment. As well, Riot will be able to more closely inspect these reports -- since 2 in every 3 of them won't be "fake" -- which will lead to more justice.
I know what you're going to say "b-but PhantomAxolotl, I get more than 6 afks, feeds, trolls, etc. in my games in a week!". People will do these things less if there is more punishment being handed out to people who deserve it. Or we get a few more.
Please just consider it.