  Kasher and Rubinstein (1997) introduced the problem of classifying the
members of a group in terms of the opinions of their potential members. This
involves a finite set of agents $N = \{1,2,\ldots,n\}$, each one having an
opinion about which agents should be classified as belonging to a specific
subgroup J. A Collective Identity Function (CIF) aggregates those opinions
yielding the class of members deemed $J$. Kasher and Rubinstein postulate
axioms, intended to ensure fair and socially desirable outcomes, characterizing
different CIFs. We follow their lead by replacing their liberal axiom by other
axioms, constraining the spheres of influence of the agents. We show that some
of them lead to different CIFs while in another instance we find an
impossibility result.
