1) Why do you participate in the Tribunal?
I think everyone loves a trainwreck, whether they like to admit it or not, reading a tribunal case is a chance to watch one and then deliver justice to whoever caused it. It's equally satisfying to pardon those that are clearly wrongfully accused or more victims than anything else.
2) What is your most requested feature in the Tribunal?
Punish Other/Praise Other
Often in tribunal cases, I will see other people in the chat log who are equally or even more abusive than the reported player. I'd like to be able to click on their name to judge any tribunal cases they have active. Additionally, I often see a LOT of players who are trying to calm a situation down or trying to counteract a troll by offering advice and encouragement to the abused. I REALLY want to be able to give these summoner's a kudos.
3) How would you make the Tribunal more effective?
We need to be able to give praise to those who stand out as remarkable players. Those people who take the time to suggest items, who buy wards consistently, and are just a huge asset to their team through their positive attitude and ability to work with others, whether or not their teammates are good or bad.
4) What is the Tribunals greatest weakness?
It focuses entirely on negative reinforcement, when studies consistently show that positive reinforcement generates better results. Negative reinforcement has the caveat of teaching people not to get caught doing undesired behavior, while positive reinforcement actually stimulates the desired behavior.
5) Would you still vote in the Tribunal if there were no IP rewards?
Yes, even though its negative reinforcement, I still believe in justice.
6) What kind of rewards would you prefer from using the Tribunal?
Justice and virtue are their own rewards, to be honest. That said, I would be satisfied if we could praise the just and the virtuous. 
Current Question of the Week [5/21/2012]:
1) If you could add one feature into the game that addresses player behavior, what would it be?
I'm probably beating a dead horse at this point, but it's really important to me. Praise/Commend/Positive Reinforcement, whatever you want to call it. We need to reward those awesome players. Make them into examples, make them into rolemodels. Make others envious of their status, so that their behavior gets emmulated. Track players with high amounts of commendations and feature their games in the spectator window. There are so many benefits to this. Other players who desire that level of attention can earn it without necessarily being super-pro, and they do it by being positive members of the community. It creates a ripple-effect where the rewards earned through good behavior become highly desired and people start getting on board. Only the most toxic players would refuse, and would be easily identified at this stage. This is an ideal scenario, granted, but one that isn't completely outside of reality.