do you get a notification if someone toxic was muted?
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Only when your report is the one that triggered the punishment.
Yes and no.
As far as I know right now, you get a notification if you reported a game that was the "final straw" in a player getting action taken against them. But lets say you reported someone in game 2 out of 3 games used against that player, you would not get a notification.
The other comments here are correct. Players are only notified about punishments if they are the one who triggers it. So, if you report someone, but do not see a notification, that does NOT mean the player did not receive a punishment. If there were two players in the match who reported the same player, the last one to click report would be the only one to see the pop-up alert.
And while it may be a bit of a language issue, just to clarify, there is a difference in muting a person on your team so that you cannot read their comments, and them being given a chat restriction by Riot. When you report someone, they are given the next punishment that they are "eligible" for, whether that is a chat restriction or a ban.
I wish they would always notify, as reporting in any game other than that 'last straw' with no notif only makes it look like a. the system is not working b. report weight dropped significantly (tho I read that recently the weight has been removed, have not seen an official source) both leading to not wanting to report anymore