The Pythagoreans define absolute justice as reciprocity, saying that justice in the unqualified sense is having done to one what one has done to another (i.e., an eye for an eye). The principle of reciprocity as they state it is oversimplified and does not agree with the ideas of distributive and remedial justice as we have explained them above. There are many situations in which reciprocity and justice are not the same (e.g., if a magistrate strikes a man, he should not be struck in return, but if an ordinary citizen strikes a magistrate, he should not only be struck in return but punished).
In certain kinds of dealings between men, however (e.g., economic activities and associations based on mutual exchange), the principle of reciprocity does apply, if it is defined as proportional reciprocity rather than reciprocity on the basis of absolute equality.
A state or community is bound together by relations between its members based on exchange of goods and services. Since people are not willing to exchange unless they get as good as they give, a principle or proportional reciprocity is necessary for guiding such relations. Proportional reciprocity takes into account the comparative skill of both parties and the comparative worth of their products, and is determined by a diagonal combination of terms. Here is an example:
A is a builder, B is a shoemaker, C is a house, D is a shoe. The builder takes the shoemaker's product (a shoe) from the shoemaker and gives his own product (a house) in return. A fair reciprocal exchange takes place if equality has been established between the goods.
