Mabrouk, Mohamed (2018): On the extension of a preorder under translation invariance.

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Abstract
This paper proves the existence, for a translationinvariant 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 translationinvariant strict preorder on ℝ which transgresses scalar invariance and also the existence of a complete translationinvariant preorder satisfying the social choice axioms strong Pareto and fixedstepanonymity 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 or under a Pareto axiom.
Item Type:  MPRA Paper 

Original Title:  On the extension of a preorder under translation invariance 
English Title:  On the extension of a preorder under translation invariance 
Language:  English 
Keywords:  Order extension, Translation invariance 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools D  Microeconomics > D7  Analysis of Collective DecisionMaking D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations D  Microeconomics > D9  Intertemporal Choice 
Item ID:  86313 
Depositing User:  Mohamed ben Ridha Mabrouk 
Date Deposited:  24 Apr 2018 08:25 
Last Modified:  13 Oct 2019 05:02 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/86313 