# An axiomatic approach to intergenerational equity

## Author

Listed:
• Toyotaka Sakai

() (Department of Economics, University of Rochester, Rochester, New York 14627, USA)

## Abstract

We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: one is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms.

## Suggested Citation

• 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.
• Handle: RePEc:spr:sochwe:v:20:y:2003:i:1:p:167-176 Note: Received: 30 August 2000/Accepted: 18 March 2002
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## References listed on IDEAS

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1. Satya Chakravarty & Diganta Mukherjee, 1999. "Measures of Deprivation and their Meaning in Terms of Social Satisfaction," Theory and Decision, Springer, pages 89-100.
2. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
3. John D. Hey & Peter J. Lambert, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 95(3), pages 567-573.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. José Alcantud, 2013. "Liberal approaches to ranking infinite utility streams: when can we avoid interference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 381-396, July.
2. repec:onb:oenbwp:y::i:95:b:1 is not listed on IDEAS
3. 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.
4. 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.
5. Markus Knell, 2005. "On the Design of Sustainable and Fair PAYG Pension Systems When Cohort Sizes Change," Working Papers 95, Oesterreichische Nationalbank (Austrian Central Bank).
6. Susumu Cato, 2009. "Characterizing the Nash social welfare relation for infinite utility streams: a note," Economics Bulletin, AccessEcon, vol. 29(3), pages 2372-2379.
7. Banerjee, Kuntal & Mitra, Tapan, 2004. "On the Continuity of Ethical Social Welfare Orders," Working Papers 04-16, Cornell University, Center for Analytic Economics.
8. repec:ebl:ecbull:v:4:y:2003:i:26:p:1-5 is not listed on IDEAS
9. Toyotaka Sakai, 2003. "Intergenerational preferences and sensitivity to the present," Economics Bulletin, AccessEcon, vol. 4(26), pages 1-5.
10. 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.
11. Kohei Kamaga & Takashi Kojima, 2009. "$${\mathcal{Q}}$$ -anonymous social welfare relations on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 405-413, September.
12. Sakamoto, Norihito, 2011. "Impossibilities of Paretian Social Welfare Functions for Infinite Utility Streams with Distributive Equity," Discussion Papers 2011-09, Graduate School of Economics, Hitotsubashi University.

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