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Public Economics Programme Discussion Paper
Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data
Frank A Cowell, Martyna Kobus and Radoslaw Kurek January 2017
Paper No' PEP 31:
Full Paper (pdf)

JEL Classification: D30; D63; D81; I31

Tags: ordinal data; inequality and risk orderings; welfare orderings; association

Decision makers and social planners are often faced with a problem of evaluating distributions of ordinal variables i.e. variables for which there are no numbers but only the ordering, such as, for example, self-reported health status, life satisfaction, working environment, quality of public goods, living conditions etc. Standard tools, namely, stochastic dominance, and inequality and risk measures, produce conclusions that can be reversed depending on the cardinalisation of an ordinal indicator which is arbitrary. Utilising the notion of integration on partially ordered sets we extend the well-known Hardy et al. (1934) result to an ordinal setting, both univariate and multivariate.