Cardinality and the Borda score

In most theoretical papers about the Borda rule, the Borda score appears as a number whose only purpose is to allow the derivation of a ranking. So, only its ordinal properties are considered; not its cardinal ones (if any). In some practical papers, the Borda score is implicitly considered to have cardinal properties. In this paper we present characterizations of the Borda rule where differences of Borda scores play an important role.