Informational requirements of social choice rules to avoid the Condorcet loser: A characterization of the plurality with a runoff

I consider informational requirements of social choice rules satisfying anonymity, neutrality, monotonicity, and efficiency, and never choosing the Condorcet loser. Depending on the number of agents and the number of alternatives, either the plurality rule or a plurality with a runoff is characterized. In some cases, the plurality rule is the most selective rule among the rules operating on the minimal informational requirement. In the other cases, each rule operating on the minimal informational requirement is a two-stage rule, and among them, a plurality with a runoff is the rule whose choice at the first stage is most selective. These results not only clarify properties of the plurality rule and a plurality with a runoff, but also explain why they are widely used in real societies.