Inequality and Polarization.

We give in this paper a formal definition of the concept of weak and strong a-polarization. We give necessary and sufficient conditions for a decision maker who respects the Lorenz order and who behaves in accordance with the expected utility model, with Yaari's dual model or with the rank-dependent expected utility model to be weakly or strongly a-polarization averse. Finally these results are applied to the specific problem of inequality measurement.