Mediation & arbitration

Justice-as-fairness is a mediation whereas justice-as-deservedness is an arbitration. 

The mediation seeks to arrive at a fair allocation, given we cannot arrive at a clear understanding of what the proper distribution ought to be; an arbitration tries to arrive at a just apportionment, given we need to know which party truly deserves what. 

A mediation tries to sort out the implications of what the contending parties had originally agreed upon. The dispute is about the implications of the agreements between the disputants. An arbitration tries to sort out the merits of what the contending parties contributed to the matter in dispute. Agreements are irrelevant to arbitrations. What matters is whose merits dominate whose with respect to the care of something they both claim.