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 note 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 note 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 the proposal of a corrected, median-independent version of the Foster-Wolfson index which always fulfills the basic transfer axioms.
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