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Infinite Utilitarianism: More Is Always Better

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  • LAUWERS, LUC
  • VALLENTYNE, PETER

Abstract

We address the question of how finitely additive moral value theories (such as utilitarianism) should rank worlds when there are an infinite number of locations of value (people, times, etc.). In the finite case, finitely additive theories satisfy both Weak Pareto and a strong anonymity condition. In the infinite case, however, these two conditions are incompatible, and thus a question arises as to which of these two conditions should be rejected. In a recent contribution, Hamkins and Montero (2000) have argued in favor of an anonymity-like isomorphism principle and against Weak Pareto. After casting doubt on their criticism of Weak Pareto, we show how it, in combination with certain other plausible principles, generates a plausible and fairly strong principle for the infinite case. We further show that where locations are the same in all worlds, but have no natural order, this principle turns out to be equivalent to a strengthening of a principle defended by Vallentyne and Kagan (1997), and also to a weakened version of the catching-up criterion developed by Atsumi (1965) and by von Weizsäcker (1965).

Suggested Citation

  • Lauwers, Luc & Vallentyne, Peter, 2004. "Infinite Utilitarianism: More Is Always Better," Economics and Philosophy, Cambridge University Press, vol. 20(2), pages 307-330, October.
  • Handle: RePEc:cup:ecnphi:v:20:y:2004:i:02:p:307-330_00
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    Cited by:

    1. Asheim, Geir B. & d'Aspremont, Claude & Banerjee, Kuntal, 2010. "Generalized time-invariant overtaking," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 519-533, July.
    2. Pivato, Marcus, 2022. "A characterization of Cesàro average utility," Journal of Economic Theory, Elsevier, vol. 201(C).
    3. Mohamed Ben Ridha Mabrouk, 2011. "Translation invariance when utility streams are infinite and unbounded," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(4), pages 317-329, December.
    4. Christian Tarsney & Teruji Thomas, 2020. "Non-Additive Axiologies in Large Worlds," Papers 2010.06842, arXiv.org.
    5. Lauwers, Luc, 2010. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 32-37, January.
    6. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    7. Jeremy Goodman & Harvey Lederman, 2024. "Maximal Social Welfare Relations on Infinite Populations Satisfying Permutation Invariance," Papers 2408.05851, arXiv.org, revised Nov 2024.
    8. Adam Jonsson, 2021. "Infinite utility: counterparts and ultimate locations," Papers 2109.01852, arXiv.org, revised Apr 2023.

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