This paper proves the existence, for any preorder on a real vector space satisfying translation invariance, of a … complete preorder extending the preorder and satisfying translation invariance. As application, the existence of a translation …

differentiable. Keywords: inequality measures, decomposability, translation invariance JEL codes: D63, H20, H21 … inequality measure is this: Translation invariance. For every x ∈X1 and any real number δ, I(x) = I(x+δ1n). (1) Finally, the … satisfies anonymity, the transfer principle, replication invariance, decomposability and translation invariance if and only if …

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one …

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one …

property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3 …