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The underlying idea behind the construction of indices of economic inequalityis based on measuring deviations of various portions of low incomes fromcertain references or benchmarks, that could be point measures like populationmean or median, or curves like the hypotenuse of the right triangle where everyLorenz curve falls into. In this paper we argue that by appropriately choosingpopulation-based references, called societal references, and distributions ofpersonal positions, called gambles, which are random, we can meaningfully unifyclassical and contemporary indices of economic inequality, as well as variousmeasures of risk. To illustrate the herein proposed approach, we put forwardand explore a risk measure that takes into account the relativity of largerisks with respect to small ones.

Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references