A short step between democracy and dictatorship

The majority rule and the hierarchically dictatorial rule are both characterized when preferences are defined over two alternatives. The majority rule is characterized in terms of seven axioms. The hierarchically dictatorial rule is characterized in terms of six of these seven axioms and the negation of the seventh, so each rule can be seen as obtained from the other by negating just one of the axioms. The pivotal axiom holds that, for societies with at least three members, the frequency with which indifference is the result of the preference aggregation must be smaller than the frequency with which one of the alternatives is declared preferred to the other.