Interestingly, one report has as much power as nine reports in a single game. The system was put in place to prevent pre-made groups ganging up on players (and to prevent spamming chat asking for reports and turning chat into a "he said/she said" sort of affair over /all), but it has the nice effect of making sure your report has meaning.
Also, Honor is a completely different system from the punishment system. You can be honored by 9 players in every game you play, but if you're also consistently reported by 1 player with a good report history in every game you play (a 100% report rate) you'll end up banned pretty quickly.
In general, however, I'd recommend against things like promising to do everything you can to get someone banned. As Oleandervine said above, that is in and of its self a report-worthy offense, and is typically more likely to further inflame the situation than it is to make the game environment more friendly. Just mute, accept that this game isn't going to be the best, and move on without engaging if you encounter this behavior again.
Yes, it sucks. Nothing you can do, however, can force that player to actually play the game properly, so making the situation worse by responding in a negative fashion doesn't gain you anything, and may make the game experience worse for the other three players on your team.