An aggregable family of multidimensional indices is characterized, in order to be consistent with a property of exogenous risk factors, i. e. health risks for which agents are not responsible for it.The family of concentration indices (or achievement indices by duality) lies in the class of polynomial functions. Necessary and suffucient conditions are stated in order to rank two health distributions thanks to the generalized concentration curves.It is shown that the properties of mirror and symetry are compatible with a sub-family of concentration indices being polynomial functions.A dominance criterion exists for this sub-family of indices, provides that the description maker is an inequality lover.