Justice cannot be objective because it is rooted in subjective intuition and opinion. But neither can justice be subjective because then it would lose its usefulness as a concept (if everyone means something different when speaking of justice, it’s useless to talk about it in the first place).
Therefore, lying somewhere between objective and subjective, justice is intersubjective. The true meaning of justice is: what a people deems to be fair.
What justice means in practice can thus be different for different peoples, whereas some principles may be universal (consider the declaration of human rights or anthropological findings on human universals for some candidate principles).
In reality, however, there does not exist any people that unanimously agrees on what is just. So what is justice when there is no consensus on it?
Among the many possible and problematic methods to reach a consensus, the least problematic appears to be going by the majority opinion. And since majority opinion is determined by a democratic process, justice is fundamentally democratic.
Now, with justice thus defined, we have to reconsider how we make moral and political arguments. For example, are you in favor of redistributing wealth and income because you find it just? Well, if a majority vote says otherwise, it is unjust and you are wrong in calling it “just.” This also implies that you will have to find better arguments than merely stating, “Because it is (not) just.”
The same holds true for the prioritization of values. Is freedom a higher good than security? Are more regulations better than less? Is homogeneity favorable to diversity? As long as we cannot predict the future to carry out the Utilitarian calculus, the answer to these questions lies in the democratic will of a people—and certainly not in some idle philosophical fantasy of justice, since the scope of philosophy ends with the formal definition.
In conclusion, questions about justice and political values can only be settled through the practice of democracy, not through ethical theory.