Suppose we are given a family of choice functions on pairs from a given
finite set (with at least three elements) closed under permutations of the
given set. The set is considered the set of alternatives (say candidates for an
office). The question is, what are the choice functions c on pairs of this set
of the following form: for some (finite) family of ``voters'', each having a
preference, i.e., a choice from each pair from the given family, c{x,y} is
chosen by the preference of the majority of voters. We give full
characterization