Exploring A New Class of Inequality Measures and Associated Value Judgements: Gini and Fibonacci-Type Sequences

John Creedy and S. Subramanian ()
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S. Subramanian: Independent Scholar; formerly, Madras Institute of Development Studies

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 5, 110-131

Abstract: Abstract This paper explores a single-parameter generalization of the Gini inequality measure. Taking the starting point to be the Borda-type social welfare function, which is known to generate the standard Gini measure, in which incomes (in ascending order) are weighted by their inverse rank, the generalisation uses a class of non-linear functions. These are based on the so-called ‘metallic sequences’ of number theory, of which the Fibonacci sequence is the best-known. The value judgements implicit in the measures are explored in detail. Comparisons with other well-known Gini measures, along with the Atkinson measure, are made. These are examined within the context of the famous ‘leaky bucket’ thought experiment, which concerns the maximum leak that a judge is prepared to tolerate, when making an income transfer from a richer to a poorer person. Inequality aversion is thus viewed in terms of being an increasing function of the leakage that is regarded as acceptable.

Keywords: Income inequality; Gini coefficient; extensions of Gini; social welfare functions; equally distributed equivalent income; Atkinson; inequality aversion; value judgements; efficiency and equity; leaky bucket experiment.; Primary 91; Secondary 91B15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13571-023-00302-y

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