The benchmark of maximum relative bipolarisation

Relative bipolarisation indices are usually constructed making sure that they achieve their minimum value of bipolarisation if and only if distributions are perfectly egalitarian. However, the literature has neglected discussing the existence of a benchmark of maximum relative bipolarisation. Consequently there is no discussion as to the implications of maximum bipolarisation for the optimal normalisation of relative bipolarisation indices either. In this note we characterize the situation of maximum relative bipolarisation as the only one consistent with the key axioms of relative bipolarisation. We illustrate the usefulness of incorporating the concept of maximum relative bipolarisation in the design of bipolarisation indices by identifying, among the family of rank-dependent Wang-Tsui indices, the only subclass fulfilling a normalisation axiom that takes into account both benchmarks of minimum and maximum relative bipolarisation.