Justice, phrased in the language of science would be a macro universe that is deterministic, in other words, set actions will always lead to set outcomes.
Basically, "what you sow you reap"
Mercy may not "rob" justice because that would destroy justice or the determinism and predictability. That is why a 3rd party is required to intervene an satisfy the demands of justice on our behalf on condition of our repentance.
The third party who pays the price is then able to extend mercy and stipulate the conditions on which remission is granted.
Animal sacrifice was only symbolic of the "great and last sacrifice" that was to come, that would be infinite and eternal and would enable the settlement to justice by the third party.
The innocent that suffers is similarly "owed" a debt by justice and that is how the books are balanced.
Interesting and sophisticated definition of justice. However Things gets bit more complicated when we add deterministic and predictability to it. “Set actions will ALWAYS lead to set outcomes”. This will eliminate the principle of free choice. This definition only makes sense to those of strong faith who believe in a bigger story of creation. Someone like average Joe is looking for more practical definitions of terms and concepts, and justice in this life, would ask can I have a definition that relates to my life? I would say "what you sow you reap" is simple enough for Joe. Still this also requires strong belief in the afterlife and Joe is not interested.
So when the judge says justice is served, what kind of definition he has in mind for the word justice. Can we have a global agreement on what this “justice” is, the one the judge is talking about? May be if we do we can live together in peace, all faiths, nations and all of humanity. Do you have any suggestions? Thanks.