Tom Gargani

PhD student ,  Aix-Marseille Université , Faculté d'économie et de gestion (FEG)

Gargani
Status
PhD candidate
PhD
Inequality measurement of ordinal variables
Since 2022, under the direction of Nicolas Gravel
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Contact
tom.gargani[at]univ-amu.fr
Address

Maison de l'économie et de la gestion d'Aix
424 chemin du viaduc, CS80429
13097 Aix-en-Provence Cedex 2

Abstract This paper provides a simple uni…ed axiomatic framework for appraising the central tendency of distributions of a single attribute (pie) among a collection of individuals depending upon the available measurement of the attribute. Two types of measurement are considered: cardinal and ordinal. For each of them, three properties are posited on an ordering of distributions of numbers among individuals. The two …rst properties are the anonymity requirement that permutations of the same list of numbers be equivalent and the weak Pareto requirement that a strict increase in the value of the variable for all individuals be favorably appraised. The third property requires that inverting the numerical measurement of the variable leads to an inversion of the ranking of the any two distributions to which the inversion is applied. The mean of a distribution is shown to be the only ordering of distributions consistent with cardinal measurability that satis…es those three requirements in the cardinal context while the median is the only such ranking consistent with ordinal measurability of the variable that sat-is…es those same requirement if the number of individuals is odd. If the number of individuals is even, then those three requirements applied to the ordinal context are shown to be inconsistent.
Keywords Consistency, Measurement, Ordinal, Cardinal, Median, Mean
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Abstract This article establishes a direct proof of the equivalence between two incomplete rankings of distributions of an ordinal attribute. The first ranking is the possibility of going from one distribution to another by a finite sequence of Hammond transfers. The second ranking is the intersection of two dominance criteria introduced by Gravel et al. (Economic Theory, 71 (2021), 33-80). The proof constructs an algorithm that provides a series of Hammond transfers, between any two distributions related by the intersection of the two dominances.
Keywords Hammond Transfers, Inequality, Algorithm
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