Multinary group identification

Group identification refers to the problem of classifying individuals into groups (e.g., racial or ethnic classification). We consider a multinary group identification model where memberships to three or more groups are simultaneously determined based on individual opinions on who belong to what groups. Our main axiom requires that membership to each group, say the group of J's, should depend only on the opinions on who is a J and who is not (that is, independently of the opinions on who is a K or an L). This shares the spirit of Arrow's independence of irrelevant alternatives and, therefore, is termed independence of irrelevant opinions. Our investigation of multinary group identification and the independence axiom reports a somewhat different message from the celebrated impossibility result by Arrow (1951). We show that the independence axiom, together with symmetry and non-degeneracy, implies the liberal rule (each person self-determines her own membership). This characterization provides a theoretical foundation for the self-identification method commonly used for racial or ethnic classifications.