Unanimous, reducible, anonymous social choice

The problem of aggregating preferences over two alternatives is considered. Three axioms are postulated: unanimity, reducibility (two divergent preferences can be replaced by their aggregation), and anonymity. It is shown that only twelve aggregation rules satisfy the three axioms: the majority rule, two myopic majority rules, three dictated rules (rules that almost always output the same outcome), and six hierarchically dictated rules (the output is determined by some priority ranking among outcomes).