IDEAS home Printed from https://ideas.repec.org/p/ver/wpaper/69-2009.html
   My bibliography  Save this paper

Variable population welfare and poverty orderings satisfying replication properties

Author

Listed:
  • Claudio Zoli

    (Department of Economics (University of Verona))

Abstract

We discuss and compare the variable population axioms of Critical Level (CL) and Population Replication Invariance (PRI) introduced in the economic and philosophical literature for evaluating distributions with different population size. We provide a common framework for analyzing these competing views considering a strengthening of the Population Replication Principle (PRP) based on Dalton's (1920) "principle of proportionate additions to persons" that requires an ordering defined over populations of the same size to be invariant w.r.t. replication of the distributions. The strong version of PRP extends the invariance condition to hold also when distributions of different population size are compared. We suggest ethically meaningful general specifications of the invariance requirement underlying the Strong PRP and characterize the associated classes of parameterized evaluation functions that include CL principles and PRI properties. Moreover, we identify a general class of evaluation functions satisfying the Strong PRP: the social evaluation ordering will be represented by the simple formula considering the product of the population size times a strictly monotonic function of the Equally Distributed Equivalent Income (EDEI). Interesting ethical properties are shown to be associated with the shape of the function transforming the EDEI. Implications for poverty measurement are investigated.

Suggested Citation

  • Claudio Zoli, 2009. "Variable population welfare and poverty orderings satisfying replication properties," Working Papers 69/2009, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:69/2009
    as

    Download full text from publisher

    File URL: http://dse.univr.it//workingpapers/WP6909.pdf
    File Function: First version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587, October.
    2. Carlson, Erik, 1998. "Mere Addition and Two Trilemmas of Population Ethics," Economics and Philosophy, Cambridge University Press, vol. 14(2), pages 283-306, October.
    3. Kanbur Ravi, 2001. "Economic Policy, Distribution and Poverty: The Nature of Disagreements," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 7(2), pages 122-145, April.
    4. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    5. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1997. "Critical-Level Utilitarianism and the Population-Ethics Dilemma," Economics and Philosophy, Cambridge University Press, vol. 13(2), pages 197-230, October.
    6. Bossert, Walter, 1990. "Population replications and ethical poverty measurement," Mathematical Social Sciences, Elsevier, vol. 20(3), pages 227-238, December.
    7. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1995. "Intertemporal Population Ethics: Critical-Level Utilitarian Principles," Econometrica, Econometric Society, vol. 63(6), pages 1303-1320, November.
    8. Kundu, Amitabh & Smith, Tony E, 1983. "An Impossibility Theorem on Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 423-434, June.
    9. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    10. Charles Blackorby & Walter Bossert & David Donaldson & Marc Fleurbaey, 1998. "Critical levels and the (reverse) repugnant conclusion," Journal of Economics, Springer, vol. 67(1), pages 1-15, February.
    11. Arrhenius, Gustaf, 2000. "An Impossibility Theorem for Welfarist Axiologies," Economics and Philosophy, Cambridge University Press, vol. 16(2), pages 247-266, October.
    12. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-177, January.
    13. Ng, Yew-Kwang, 1986. "Social criteria for evaluating population change: An alternative to the Blackorby-Donaldson criterion," Journal of Public Economics, Elsevier, vol. 29(3), pages 375-381, April.
    14. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-526, June.
    15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    16. Satya R. Chakravarty, 2019. "Ethically Flexible Measures of Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 13-26, Springer.
    17. Bossert, Walter, 1990. "Social evaluation with variable population size: an alternative concept," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 143-158, April.
    18. Amiel,Yoram & Cowell,Frank, 1999. "Thinking about Inequality," Cambridge Books, Cambridge University Press, number 9780521466967, October.
    19. repec:bla:jpbect:v:4:y:2002:i:3:p:347-68 is not listed on IDEAS
    20. Satya Chakravarty & Ravi Kanbur & Diganta Mukherjee, 2006. "Population growth and poverty measurement," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 471-483, June.
    21. repec:bla:jecsur:v:11:y:1997:i:2:p:123-62 is not listed on IDEAS
    22. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    23. John BROOME, 1992. "The Value of Living," Discussion Papers (REL - Recherches Economiques de Louvain) 1992021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    24. Ng, Yew-Kwang, 1989. "What Should We Do About Future Generations?," Economics and Philosophy, Cambridge University Press, vol. 5(2), pages 235-253, October.
    25. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    26. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    27. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    28. Blackorby, Charles & Donaldson, David, 1984. "Social criteria for evaluating population change," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 13-33, November.
    29. Blakorby, Charles & Donaldson, David, 1980. "Ethical Indices for the Measurement of Poverty," Econometrica, Econometric Society, vol. 48(4), pages 1053-1060, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Subramanian S., 2017. "On Comprehensively Intermediate Measures of Inequality and Poverty, with an Illustrative Application to Global Data," Journal of Globalization and Development, De Gruyter, vol. 8(2), pages 1-18, December.
    2. Marc Fleurbaey & Domenico Moramarco & Vito Peragine, 2024. "Measuring inequality and welfare when some inequalities matter more than others," Working Papers ECARES 2024-15, ULB -- Universite Libre de Bruxelles.
    3. Sunil Rajpal & Rockli Kim & Lathan Liou & William Joe & S. V. Subramanian, 2020. "Does the Choice of Metric Matter for Identifying Areas for Policy Priority? An Empirical Assessment Using Child Undernutrition in India," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 152(3), pages 823-841, December.
    4. Marc Fleurbaey & Domenico Moramarco & Vito Peragine, 2024. "Measuring inequality and welfare when some inequalities matter more than others," Working Papers 674, ECINEQ, Society for the Study of Economic Inequality.
    5. S. Subramanian & Diganta Mukherjee, 2018. "On Intermediate Headcount Indices Of Poverty," Bulletin of Economic Research, Wiley Blackwell, vol. 70(4), pages 443-451, October.
    6. Walter Bossert & Susumu Cato & Kohei Kamaga, 2023. "Thresholds, critical levels, and generalized sufficientarian principles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1099-1139, May.
    7. Marc Fleurbaey & Domenico Moramarco & Vito Peragine, 2024. "Measuring inequality and welfare when some inequalities matter more than others," SERIES 03-2024, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Sep 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter Bossert & Susumu Cato & Kohei Kamaga, 2022. "Generalized Poverty-gap Orderings," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(1), pages 189-215, November.
    2. Sreenivasan Subramanian, 2004. "Indicators of Inequality and Poverty," WIDER Working Paper Series RP2004-25, World Institute for Development Economic Research (UNU-WIDER).
    3. Kohei Kamaga, 2016. "Infinite-horizon social evaluation with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 207-232, June.
    4. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2002. "Critical-Level Population Principles and the Repugnant Conclusion," Cahiers de recherche 2002-15, Universite de Montreal, Departement de sciences economiques.
    5. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2006. "Population Ethics," Cahiers de recherche 2006-15, Universite de Montreal, Departement de sciences economiques.
      • BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2006. "Population Ethics," Cahiers de recherche 14-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Jean–Yves Duclos & Phillipe Grégoire, 2002. "Absolute and Relative Deprivation and the Measurement of Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(4), pages 471-492, December.
    7. Charles Blackorby & Walter Bossert & David Donaldson, 2002. "Population Principles with Number‐Dependent Critical Levels," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 4(3), pages 347-368, July.
    8. Satya R. Chakravarty & Pietro Muliere, 2004. "Welfare indicators: a review and new perspectives. 2. Measurement of poverty," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 247-281.
    9. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    10. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    11. Cockburn, John & Duclos, Jean-Yves & Zabsonré, Agnès, 2014. "Is global social welfare increasing? A critical-level enquiry," Journal of Public Economics, Elsevier, vol. 118(C), pages 151-162.
    12. Dean Spears & Mark Budolfson, 2021. "Repugnant conclusions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 567-588, October.
    13. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    14. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    15. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    16. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    17. John COCKBURN & Jean-Yves DUCLOS & Agnès ZABSONRÉ, 2011. "Is the value of humanity increasing? A critical-level enquiry," Working Papers I13, FERDI.
    18. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    19. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    20. BLACKORBY, Charles & BOSSERT, Walter & DONALDSON, David, 2003. "Population Ethics and the Value of Life," Cahiers de recherche 05-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

    More about this item

    Keywords

    Variable Population Social Choice; Population Replication; Welfare Measurement; Poverty Measurement.;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ver:wpaper:69/2009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Michael Reiter (email available below). General contact details of provider: https://edirc.repec.org/data/isverit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.