Distributive justice always involves two persons and two things. Its aim is to distribute the things in such a way that the relative positions of the two persons prior to the transaction are maintained after the transactions, i.e., the thing is divided proportionally to the merit of the persons concerned, always remembering that the standard of merit for individuals varies in different kinds of states (e.g., in a democracy it is freedom, in an oligarchy it is wealth, in an aristocracy it is virtue), and that a distribution can be made between unequal individuals.
Distributive justice is best viewed as a form of discrete or geometrical proportion. For example, there are two men, A and B, and two things, C and D. Assume that A and B are equal in merit and C and D equal in value. This gives the equation, A : B = C : D. In accordance with distributive justice, all of C is given to A and all of D is given to B, and the situation after the transaction is, A + C : B + D = A : B. That is the relative positions of A and B are the same before and after the transaction. In this kind of case justice is a mean between giving A or B more or less than their rightful shares.
In cases involving distribution, justice is what is proportional and injustice is violation of proportion. A man who acts unjustly has more than his share, while a man who is treated unjustly has less.