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I think that I agree that justice is opposed to arbitrary decisions. But I want to register two concerns.

First, all of you keep talking about rules and principles that somehow determine justice. As I said before, this sounds a little bit like a certain idea of natural science in which there are lower level laws and higher level laws. The lower level laws are subsumed under the higher level laws. In the end we have a beautiful structure that logically follows from a few first principles. The ideal here is a kind of universality or universalism.

But is that the way justice works? (Or science for that matter?) Can we really apply the law-like model? I think philosophers call it the nomological model. Does it work when we're talking about morality in general or justice in particular? I'm not at all sure.

Second, it seems to me that there may still be arbitrariness left in justice as you describe it. You may be able to eliminate arbitrariness in the application of your rules, and you may be able to create consistent, logical theories of justice. But what about the foundations? When you finally get to the highest principles, the ultimate values on which the system is based, can you still eliminate the arbitrariness? Perelman didn't think so. Keep that in mind.