Corrective or remedial justice pertains to both voluntary and involuntary transactions. In cases of the first kind, two parties voluntarily entered into a contract or relationship and injury was done to one party. The duty of the judge in such a case is not to punish, but to remedy, and it is not relevant whether both or either parties to the case are good or bad men. The law treats both parties as equals, determines what damage has been done and to whom, and tries to restore the equilibrium which existed before the transaction.
As in cases pertaining to voluntary justice, the terms "gain" and "loss" are also used in discussing involuntary transactions, although they are not always the most appropriate terms and may at times be misleading. Their meaning will be illustrated by the following example — a brawl takes place in which one man stabs another, the man who did the stabbing may be said to have gained while the man who was wounded has suffered a loss. In cases involving involuntary transactions the law is still concerned with restoring a balance, but since most involuntary transactions are criminal acts, it is necessary to interpret gain and loss in the broadest sense.
Corrective justice takes the form of an arithmetical proportion (also known as an arithmetical progression). Let us say that there are two equal parties, A and B. After a certain transaction, A has injured B to the extent of C, and their relation is A C, B - C. To restore the balance, the judge takes C from A and gives it to B, creating a new relationship. A C - C = B - C + C, an arithmetical mean between gain and loss in which the relative positions of the parties is once again the same.
The Aristotelian concept of corrective justice is illustrated by the following diagram:
A E A' B___________ B' D C F C'
A transaction (e.g., a theft) takes place in which CC' injuries AA' to the extent or value AE, i.e., CC' takes AE from AA'. After the transaction, the injured party is reduced to EA' while the injurer is increased by DC (that which he has taken) to DCC'. The judge keeps in mind the mean BB' and sees the inequality between EA' and DCC'. He determines the value of AE (= DC and DF) and gives to the injured party that which will restore the balance or mean while taking from the injuring party that which he has that exceeds the mean.