# A characterization and an impossibility of finite length anonymity for infinite generations

## Author

Listed:
• Sakai, Toyotaka

## Abstract

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation (Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an "almost" fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.

## Suggested Citation

• Sakai, Toyotaka, 2010. "A characterization and an impossibility of finite length anonymity for infinite generations," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 877-883, September.
• Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:877-883
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File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(10)00075-3
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## References listed on IDEAS

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1. Fleurbaey, Marc & Michel, Philippe, 2001. "Transfer principles and inequality aversion, with an application to optimal growth," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 1-11, July.
2. Toyotaka Sakai, 2006. "Equitable Intergenerational Preferences on Restricted Domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 41-54, August.
3. Fleurbaey, Marc & Michel, Philippe, 2003. "Intertemporal equity and the extension of the Ramsey criterion," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 777-802, September.
4. Christopher Chambers, 2009. "Intergenerational equity: sup, inf, lim sup, and lim inf," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 243-252, February.
5. Geir B. Asheim & Kuntal Banerjee, 2010. "Fixed‐step anonymous overtaking and catching‐up," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 149-165, March.
6. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 393-414, September.
7. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
8. Toyotaka Sakai, 2003. "An axiomatic approach to intergenerational equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(1), pages 167-176.
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## Citations

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Cited by:

1. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
2. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 393-414, September.
3. Adachi, Tsuyoshi & Cato, Susumu & Kamaga, Kohei, 2014. "Extended anonymity and Paretian relations on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 24-32.
4. Alcantud, José Carlos R., 2013. "Fuzzy sets from the ethics of social preferences," MPRA Paper 53549, University Library of Munich, Germany.

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### Keywords

Intergenerational equity Finite length anonymity Infinite dimension Diamond' s impossibility theorem Social choice;

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