When Are Goods More Goods ?

Abstract

It is here implied that if A is chosen rather than B, A represents more (or not fewer) goods than B (even if A contains less of some individual goods). This sounds rather like the converse of the axiom of nonsaturation, which states that if A contains more goods than B in the vector sense (i.e. more of some goods and less of none) then A will be chosen rather than B. It is not that coniverse, but an alternative definition of more goods . Professor Johnson defines more goods in terms of choice, and when he assumes that more than in this sense is an asymmetric relation, he is in effect stating in a roundabout way the axiom that choice is consistent. Mr. Lancaster has pointed out2 that if we assume strong ordering the substitution theorem can be derived from the axiom of consistency alone, while if we assume weak ordering the axiom of non-saturation is also necessary. Professor Johnson in fact uses both axioms, but makes it appear that both follow from his definition of goods . They are, on the contrary, quite independent ; the illusion of a close relationship between them arises from the ambiguity introduced by the two definitions-the vector definition and the choice definition-of more goods.