There are basically 5 classifications of people in this situation.
Innocent people that do not fear it. These people understand the purpose of the tribunal, and know that, if for some reason they end up under its hammer, they deserved it. These people will never post ban appeals, unless it is truly for something they are innocent for. These are less likely to even be banned in the first place, as they're not likely that Riot staff would, after reading the details, insist a permaban.
Innocent people that do fear it. These are the people that don't fully understand what the tribunal is and does. They fear getting banned, but they also would not under normal circumstances do anything to be banned. These are unfortunately the people who are most effected negatively by it.
Guilty ones that fear it. These are people that know they're likely going to get caught, because they know they do wrong. These are likely also the ones that tend to post appeals on normal permaban cases. These people, although not ruining the game for others, still provide negative atmospheres for other players.
Guilty ones that do not fear it. The person thinks that the tribunal is a joke, or does not work, and will act as they please. These are the people that, when banned, end up raging in forums (I do not have to post any names... as we all know at least one...) These are the people that we do not want playing the game at all, because they simply believe that they have the right to do what they want. (a lot of people from the 3rd group, that start spending a lot of money, tend to move here, as they think that them paying money makes them immune)
The final group, is similar to the previous... as they are guilty and also do not fear it, but for different reasons. These are the people, that will purposely cause issues for other players... continuously. Trolls. The people that will, when banned, not say a word, not ask for an appeal. simply create another account, and repeat the same actions that got them banned. These people are often from the 4th group, who have raged their hearts out in the forums, and have given up trying to get their level 30 account back, and simply set out to ruin the game for others.
In summary, I believe this works for the most part. The ones who are guilty of doing wrong, are the ones who get banned. The ones who are innocent, do not. Unfortunately, as the second group, there are some innocent players, that do not fully understand this, and therefore play in fear of being banned. It is simply something that they will learn, eventually, becoming part of the first group.
there are unfortunately, a few that move from the top down, rather than the bottom up. People that are otherwise innocent, classified under group two, getting a warning because they got upset a couple games, and believing they have done nothing wrong, start to do wrong, as they think that the system is unbalanced... then progress downward.
The tribunal, works as good as anything can, if not better, for a justice system imposed on an otherwise completely anonymous system.
There's not quite 100% evidence presented. When you see 4 different cases, totaling 12 reports, you see 4 cases. you do not see the other thousand games where the player was an angel. This is the one downfall of the system, but also a strength. As if you see that 4/1000 are infractions, you would simply be more lenient, because they are normally good.
RL EXAMPLE FOLLOWING:
The fact is, just because someone spent 60 years of their life not breaking the law, doesn't mean they should be held any more innocent when they do, than someone who is only 20.
The tribunal provides a completely unique system. As it does not base itself off of rules, it is more off of guidelines. This makes it down to what each individual voter's preferences are.
If they would not enjoy a game with a person of that attitude/actions... punish.
if they think that its not really a problem that they did that, pardon.
being punished by the tribunal means that the majority of players that read your case simply said "I dont want to play a game with someone who does that."
Because it is not staff directly deciding on your fate, it is the players, it becomes an amazingly unique, and an effective tool, at drawing attention. In truth, if the Tribunal was more... not quite advertised, but known, League of Legends could quickly multiply in size. Most players of games would jump at the chance to be able to finally react on the trolls and ragers that they hate so much. There's not a good gamer out there that does not wish they had a BAN button on their keyboard, to get rid of the people that ruin the game... this is pretty darn close to one.