Riskiness for sets of gambles

Moti Michaeli

Aumann--Serrano (2008) and Foster--Hart (2009) suggest two new riskiness measures, each of which enables one to elicit a complete and objective ranking of gambles according to their riskiness. Hart (2011) shows that both measures can be obtained by looking at a large set of utilityfunctions and applying "uniform rejection criteria" to rank the gambles in accordance with this set of utilities. We use the same "uniform rejection criteria" to extend these two riskiness measures to the realm of uncertainty and develop complete and objective rankings of sets ofgambles, which arise naturally in models of decision making under uncertainty.

March, 2012