Just a suggestion:

Give extra IP to a case based on how many people have skipped the case in the Tribunal. I think it's safe to assume that the skipped cases are the ones which are more difficult for people to come to the right conclusion, so those who spend extra time on going through every game of a more difficult case should be given some sort of incentive to do so. For example, 1 IP for every 10 times the Skip button has been pressed for that case. (With some maximum such as 10 bonus IP)
At the same time, I don't feel quite as bad as skipping the case and handing it off to someone else to spend extra time on, so I can focus on more clear-cut cases.