The underlying idea behind the construction of indices of economic inequality
is based on measuring deviations of various portions of low incomes from
certain references or benchmarks, that could be point measures like population
mean or median, or curves like the hypotenuse of the right triangle where every
Lorenz curve falls into. In this paper we argue that by appropriately choosing
population-based references, called societal references, and distributions of
personal positions, called gambles, which are random, we can meaningfully unify
classical and contemporary indices of economic inequality, as well as various
measures of risk. To illustrate the herein proposed approach, we put forward
and explore a risk measure that takes into account the relativity of large
risks with respect to small ones.Comment: 29 pages, 4 figure
