Axiomatic characterisations of the basic best–worst rule

We show that reinforcement and top–bottom cancellation imply anonymity, and that the basic best–worst rule can be characterised by neutrality, continuity, reinforcement, and top–bottom cancellation. Additionally, we directly characterise the basic best–worst rule by neutrality, reinforcement, top–bottom non-negativity, and top–bottom cancellation. Top–bottom non-negativity requires that if the difference in number between the individuals preferring a certain alternative as their best and worst alternatives respectively is strictly negative, then that alternative is not included in the social choice.