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# Translation invariance when utility streams are infinite and unbounded

## Author

Listed:
• Mabrouk, Mohamed

## Abstract

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one applies the same translation to both. This axiom is significant in the characterization of utilitarian criteria in finite dimension. This characterization is achieved thanks to the "weak weighted utilitarianism theorem".The objective here is to propose a generalization of this theorem in a space of infinite and unbounded utility streams. A consequence of the suggested generalization is that, in the context of intergenerational choice, every maximal point with respect to a paretian utilitarian order granting comparable considerations to the present and the future, is also a maximal point with respect to some future-oriented criterion.

## Suggested Citation

• Mabrouk, Mohamed, 2008. "Translation invariance when utility streams are infinite and unbounded," MPRA Paper 18523, University Library of Munich, Germany, revised 01 Oct 2009.
• Handle: RePEc:pra:mprapa:18523
as

File URL: https://mpra.ub.uni-muenchen.de/18523/1/MPRA_paper_18523.pdf
File Function: original version
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## References listed on IDEAS

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Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Mabrouk, Mohamed, 2018. "On the Extension and Decomposition of a Preorder under Translation Invariance," MPRA Paper 90537, University Library of Munich, Germany.
2. Mabrouk, Mohamed, 2009. "On the extension of a preorder under translation invariance," MPRA Paper 15407, University Library of Munich, Germany.
3. Efe A. Ok & Gil Riella, 2014. "Topological Closure of Translation Invariant Preorders," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 737-745, August.

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### Keywords

Translation invariance; Infinite utility streams; Utilitarianism; Intergenerational equity;
All these keywords.

### JEL classification:

• D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other
• D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
• D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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