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.