  Many classical social choice correspondences are resolute only in the case of
two alternatives and an odd number of individuals. Thus, in most cases, they
admit several resolute refinements, each of them naturally interpreted as a
tie-breaking rule, satisfying different properties. In this paper we look for
classes of social choice correspondences which admit resolute refinements
fulfilling suitable versions of anonymity and neutrality. In particular,
supposing that individuals and alternatives have been exogenously partitioned
into subcommittees and subclasses, we find out arithmetical conditions on the
sizes of subcommittees and subclasses that are necessary and sufficient for
making any social choice correspondence which is efficient, anonymous with
respect to subcommittees, neutral with respect to subclasses and possibly
immune to the reversal bias admit a resolute refinement sharing the same
properties.
