Before revision:  Therefore, we introduce a completely novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective scores. We introduce and investigate corresponding notions of multi-objective elicitability, which may prove beneficial in various applications beyond finance. In particular, we prove that conditional elicitability of two functionals implies joint multi-objective elicitability with respect to the lexicographic order on \mathbb{R}^2 , which makes it applicable in the context of CoVaR, MES or (CoVaR, CoES), together with VaR.
After revision:  Therefore, we introduce a completely novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective elicitability however, relying on multivariate scores equipped with an order, leads to a positive result when using the lexicographic order on \mathbb{R}^2 , which makes it applicable in the context of CoVaR, MES or (CoVaR, CoES), together with VaR.