Good and Bad Objects : Cardinality-Based Rules

We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize three cardinality-based rules which arise naturally in this dichotomous setting. They are what we call the symmetric difference rule, the lexicographic good-bad rule, and the lexicographic bad-good rule. Each of these rules induces a unique additive separable preference relation over the set of all groups of objects