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On the extension of a preorder under translation invariance

Mabrouk, Mohamed (2009): On the extension of a preorder under translation invariance.

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Abstract

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-invariant complete preorder on infinite utility streams satisfying strong Pareto and fixed-step anonymity, is established.

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