On the extension of a preorder under translation invariance
Mohamed Mabrouk ()
MPRA Paper from University Library of Munich, Germany
Abstract:
This paper proves the existence, for a translation-invariant preorder on a divisible commutative group, of a complete preorder extending the preorder in question and satisfying translation invariance. We also prove that the extension may inherit a property of continuity. As an application, we prove the existence of a complete translation-invariant strict preorder on ℝ which transgresses scalar invariance and also the existence of a complete translation-invariant preorder satisfying the social choice axioms strong Pareto and fixed--step-anonymity on a set X^{ℕ₀}, where X is a divisible commutative group. Moreover, the two extension results are used to make scalar invariance appear as a consequence of translation invariance under a continuity requirement.
Keywords: Order extension; Translation invariance (search for similar items in EconPapers)
JEL-codes: C60 C65 D7 D71 D9 (search for similar items in EconPapers)
Date: 2018-04-19
New Economics Papers: this item is included in nep-mic
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https://mpra.ub.uni-muenchen.de/86564/1/MPRA_paper_86313.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/86564/8/MPRA_paper_86564.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/86567/16/MPRA_paper_86567.pdf revised version (application/pdf)
Related works:
Working Paper: On the extension of a preorder under translation invariance (2018)
Working Paper: On the extension of a preorder under translation invariance (2009)
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