Quantifying the degree of risk aversion of spectral risk measures

I propose a functional on the space of spectral risk measures that quantifies their degree of risk aversion''. This quantification formalizes the idea that some risk measures are more risk-averse’’ than others. I construct the functional using two axioms: a normalization on the space of CVaRs and a linearity axiom. I present two formulas for the functional and discuss several properties and interpretations.