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I agree with what you say, but it doesn't go far enough.

It's possible that a dictator could treat equal cases equally badly. He might not act arbitrarily, but he would still be unjust by any widely accepted criterion.

We need a lot more than non-arbitrary treatment if we are to define justice.

But, again, I agree that the fight against arbitrary treatment is important. Arbitrary rule exists in many parts of the world today. But eliminating it doesn't necessarily give us justice.