alt Hacker News> It’s highly unusual to have some sort of judicial process.
Every forum I ever used prior to Reddit had a ban appeal process, as did most game servers. For a few games reading the ban appeals could be more fun than playing the actual game. This was usually moderators making executive decisions based on a user-submitted form, but it was better than nothing.
Reddit also has a ban appeals process. But it's the same people you're appealing to - the mods.
Speaking for myself I generally will unban if people are nice and express understanding for why they were banned.