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On the extension of a preorder under translation invariance

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  • Mabrouk, Mohamed

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 or under a Pareto axiom.

Suggested Citation

  • Mabrouk, Mohamed, 2018. "On the extension of a preorder under translation invariance," MPRA Paper 86313, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:86313
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    References listed on IDEAS

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    More about this item

    Keywords

    Order extension; Translation invariance;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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