The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement
Research on Economic Inequality
ISBN: 978-1-78714-522-1, eISBN: 978-1-78714-521-4
Publication date: 10 October 2017
Abstract
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.
Keywords
Acknowledgements
Acknowledgments
I would like to thank Jacques Silber and an anonymous referee for very helpful comments.
Citation
Yalonetzky, G. (2017), "The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement", Bandyopadhyay, S. (Ed.) Research on Economic Inequality (Research on Economic Inequality, Vol. 25), Emerald Publishing Limited, Leeds, pp. 51-62. https://doi.org/10.1108/S1049-258520170000025002
Publisher
:Emerald Publishing Limited
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