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Infinite-horizon social evaluation with variable population size

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Abstract

We present an infinite-horizon extension of the framework of variable-population social choice. Our first main result is the welfarism theorem using the axiom of intratemporal anonymity. By this theorem, the ranking of social alternatives is determined by an intratemporally anonymous and finitely complete quasi-ordering [which we call social welfare relation (SWR)] defined on the set of all streams of utility vectors of generations. We introduce three SWRs: the critical-level generalized utilitarian (CLGU) SWR, the critical-level generalized overtaking (CLGO) SWR, and the critical-level generalized catching-up (CLGC) SWR. They are infinite-horizon extensions of the critical-level generalized utilitarianism. We characterize (in terms of subrelation) the CLGU SWR with five axioms: Strong Pareto, Finite Anonymity, Weak Existence of Critical Levels, Restricted Continuity, and Existence Independence. Further, the CLGO and the CLGC SWRs are characterized by adding consistency axioms. We also present infinite-horizon reformulations of some population ethics axioms. In particular, we characterize the CLGO and the CLGC SWRs associated with a positive critical level by using the axiom of avoidance of the repugnant conclusion.

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Notes

  1. See Asheim (2010) and Lauwers (2014) for reviews of the literature.

  2. See Blackorby et al. (2002, 2005) for reviews of the literature.

  3. A variant of the critical-level leximin ordering is proposed by Blackorby et al. (1996).

  4. Boucekkine et al. (2011) apply the CLGU ordering to an endogenous growth model by using time discounting and assuming that a transformation of utility levels is the identity mapping. However, the axiomatic foundation of their evaluation relation is not discussed.

  5. The impossibility of explicit construction of Paretian and anonymous orderings for infinite utility streams was first suggested by Fleurbaey and Michel (2003).

  6. The Suppes–Sen grading principle was introduced by Suppes (1966) and further analyzed by Sen (1970) in the finite- and fixed-population framework.

  7. A characterization in terms of subrelation means a characterization of the class of all SWRs that include the SWR considered as a subrelation. The notion of subrelation is explained in Sect. 3.1.

  8. For a discussion of neutrality and its normalization to zero, see Broome (1993).

  9. A quasi-ordering is a reflexive and transitive binary relation.

  10. See also d’Aspremont (1985, 2007) and d’Aspremont and Gevers (1977) for similar results in the finite- and infinite-horizon fixed-population frameworks.

  11. See also Blackorby et al. (1995, 2002, 2005) for the critical-level generalized utilitarian ordering.

  12. Their axioms also appear in Blackorby et al. (1995, 1998a, 1999).

  13. An ordering extension of a given binary relation is an ordering that includes it as a subrelation.

  14. See also Asheim and Banerjee (2010), Asheim and Tungodden (2004), and Basu and Mitra (2007) for similar axioms in the framework of ranking infinite utility streams.

  15. An axiom similar to IC is presented by Asheim and Tungodden (2002) in the framework of ranking infinite utility streams.

  16. See also Carlson (1998) for other related criticisms.

  17. Blackorby et al. (1997, footnote 35) note that Thomas Hurka also made this point.

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Acknowledgments

I am grateful to two anonymous referees and an editor of this journal. Their detailed comments and suggestions have greatly improved the current version of this paper. I also thank the participants at the 11th Meeting of the Society for Social Choice and Welfare for their comments. All remaining errors are my own. This study is partly supported by a Grant-in-Aid for Young Scientists (B) (No. 23730196) from the Ministry of Education, Science, Sports, and Culture, Japan.

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  1. Faculty of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554, Japan

    Kohei Kamaga

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Kamaga, K. Infinite-horizon social evaluation with variable population size. Soc Choice Welf 47, 207–232 (2016). https://doi.org/10.1007/s00355-016-0953-4

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