Characterizing best-worst voting systems in the scoring context

An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best-worst” choice; characterize a class of “best-worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval-disapproval systems.