The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement

The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster–Wolfson index. This study shows that the use of the median in the design and computation of relative bipolarisation indices is both unnecessary and problematic. It is unnecessary because we can rely on existing well-behaved, median-independent indices. It is problematic because, as the study shows, median-dependent indices violate the basic transfer axioms of bipolarisation (defining spread and clustering properties), except when the median is unaffected by the transfers. The convenience of discarding the median from index computations is further illustrated with a numerical example in which median-independent indices rank distributions according to the basic transfer axioms while median-dependent indices do not.