Few papers in the literature on inequality measurement deal with uncertainty, particularly when the ranking of cohorts may not be fixed. We present a set of axioms implying such a class of inequality measures under uncertainty that is a one-parameter extension of the generalized Gini mean over...

We introduce the concept of a conditional small world event domain--an extension of Savage's [The Foundations of Statistics, Wiley, New York, 1954] notion of a 'small world'--as a self-contained collection of comparable events. Under weak behavioral conditions we demonstrate probabilistic...