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Social choice with approximate interpersonal comparison of welfare gains

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  • Pivato, Marcus

Abstract

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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  • Pivato, Marcus, 2011. "Social choice with approximate interpersonal comparison of welfare gains," MPRA Paper 32252, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:32252
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    References listed on IDEAS

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    1. Pivato, Marcus, 2010. "Risky social choice with approximate interpersonal comparisons of well-being," MPRA Paper 25222, University Library of Munich, Germany.
    2. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    3. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541 Elsevier.
    4. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    5. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
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    15. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    16. Pivato, Marcus, 2013. "Social welfare with incomplete ordinal interpersonal comparisons," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 405-417.
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    19. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
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    Cited by:

    1. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
    2. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    3. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    4. Pivato, Marcus, 2013. "Social welfare with incomplete ordinal interpersonal comparisons," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 405-417.

    More about this item

    Keywords

    utilitarian; interpersonal comparisons; difference order; cardinal utility; linearly ordered abelian group;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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