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Social choice with approximate interpersonal comparison of welfare gains

  • Pivato, Marcus

Suppose it is possible to make approximate interpersonal comparisons of welfare gains and losses. Thus, if w, x, y, and z are personal psychophysical states (each encoding all ethically relevant information about the physical and mental state of a person), then it sometimes possible to say, ``The welfare gain of the state change w --> x is greater than the welfare gain of the state change y --> z.'' We can represent this by the formula ``(w --> x)> (y --> z)'', where `>' is a `difference preorder': an incomplete preorder on the space of all possible personal state changes. A `social state change' is a bundle of personal state changes. A `social difference preorder' (SDP) is an incomplete preorder on the space of social state changes, which satisfies Pareto and Anonymity axioms. The `minimal' SDP is the natural extension of the Suppes-Sen preorder to this setting; we show that it is a subrelation of every other SDP. The `approximate utilitarian' SDP ranks social state changes by comparing the sum total utility gain they induce, with respect to all `utility functions' compatible with `>'. The `net gain' preorder ranks social state changes by comparing the aggregate welfare gain they induce upon various subpopulations. We show that, under certain conditions, all three of these preorders coincide.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32252.

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Date of creation: 14 Jul 2011
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Handle: RePEc:pra:mprapa:32252
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  1. Fine, Ben, 1975. "A Note on "Interpersonal Aggregation and Partial Comparability"," Econometrica, Econometric Society, vol. 43(1), pages 169-72, January.
  2. Basu, Kaushik & Mitra, Tapan, 2005. "On the Existence of Paretian Social Welfare Relations for Infinite Utility Streams with Extended Anonymity," Working Papers 05-06, Cornell University, Center for Analytic Economics.
  3. Blackorby, Charles, 1975. "Degrees of Cardinality and Aggregate Partial Orderings," Econometrica, Econometric Society, vol. 43(5-6), pages 845-52, Sept.-Nov.
  4. Kaushik Basu & Tapan Mitra, 2003. "Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian," Econometrica, Econometric Society, vol. 71(5), pages 1557-1563, 09.
  5. M. Fleurbaey & P. Michel, 1997. "Intertemporal equity and the extension of the Ramsey criterion," THEMA Working Papers 97-11, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Pivato, Marcus, 2010. "Approximate interpersonal comparisons of well-being," MPRA Paper 25224, University Library of Munich, Germany.
  7. Sen, Amartya K, 1972. "Interpersonal Comparison and Partial Comparability: A Correction," Econometrica, Econometric Society, vol. 40(5), pages 959, September.
  8. Manel Baucells & Lloyd S. Shapley, 2000. "Multiperson Utility," Econometric Society World Congress 2000 Contributed Papers 0078, Econometric Society.
  9. Pivato, Marcus, 2011. "Additive representation of separable preferences over infinite products," MPRA Paper 28262, University Library of Munich, Germany.
  10. Pivato, Marcus, 2010. "Risky social choice with approximate interpersonal comparisons of well-being," MPRA Paper 25222, University Library of Munich, Germany.
  11. Charles M. Harvey & Lars Peter Østerdal, 2007. "Cardinal Scales for Public Health Evaluation," Discussion Papers 07-01, University of Copenhagen. Department of Economics.
  12. Patrick Suppes & Muriel Winet, 1955. "An Axiomatization of Utility Based on the Notion of Utility Differences," Management Science, INFORMS, vol. 1(3-4), pages 259-270, 04-07.
  13. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  14. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  15. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
  16. Arrow, Kenneth J, 1977. "Extended Sympathy and the Possibility of Social Choice," American Economic Review, American Economic Association, vol. 67(1), pages 219-25, February.
  17. Pivato, Marcus, 2010. "Aggregation of incomplete ordinal preferences with approximate interpersonal comparisons," MPRA Paper 25271, University Library of Munich, Germany.
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