Ordering Infinite Utility Streams

Département de Sciences Economiques and CIREQ, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal QC, Canada H3C 3J7
Journal of Economic Theory (Impact Factor: 1.24). 02/2007; 135(1):579-589. DOI: 10.1016/j.jet.2006.03.005
Source: RePEc

ABSTRACT We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditions. First, we provide a characterization of all ordering extensions of the generalized Lorenz criterion as the only strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. Second, we offer a characterization of an infinite-horizon extension of leximin obtained by adding an equity-preference axiom to strong Pareto and finite anonymity.

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Available from: Walter Bossert, Aug 04, 2015
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    • "Theorems 1 and 2 in Bossert et al. (2007) prove that both PDT and SEP are compatible with orderings on R N that verify SP and AN. Nevertheless, the literature on egalitarianism in the evaluation of infinite streams of utilities has provided evidences that the Pigou–Dalton transfer principle, as well as the Lorenz domination principle, conflict with weak forms of continuity and rationality even in the absence of Paretian restrictions (Sakai 2006; Hara et al. 2008, Theorems 1, 2). "
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    ABSTRACT: We are concerned with the problem of aggregating infinite utility streams and the possible adoption of consequentialist equity principles when using numerical evaluations of the streams. We find a virtually universal incompatibility between the Basu-Mitra approach (that advocates for social welfare functions and renounces continuity assumptions) and postulates that capture various forms of strict preference for a reduction in inequality like the Strong Equity Principle, the Pigou-Dalton Transfer principle, or Altruistic Equity.
    11/2013; 1(2). DOI:10.1007/s40505-013-0005-5
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    • "In all the axioms above, when W(y) > W(x) is requested in place of W(y) W(x) we refer to HE + , HEF + , RNS + , ... Property HE + is used by d'Aspremont and Gevers (1977) under the term extremist equity. HE(a) + is called strict equity preference in Bossert et al. (2007) "
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    ABSTRACT: Two factors influence the resolution of the conflict among infinite generations: the consistency/ethical postulates requested; and the utilities that each generation can possess. We contribute to qualifying the Basu-Mitra approach to this problem, that concerns social welfare functions. Firstly we examine efficiency and strengthened forms of Hammond Equity for the Future both when the feasible utilities are [0,1] and natural numbers. This complements Banerjee (Economics Letters, 2006) and Alcantud and Garcia- Sanz (Economics Letters, 2010). Secondly, we analyze the possibility of combining Pareto-efficiency and the spirit of the Hammond Equity principle for both specfications of the feasible utilities. Here the case study is richer since we analyze four different versions of this principle. We conclude that the Anonymity, Hammond Equity for the Future, and Hammond Equity ethics can be combined with weak specifications of the Pareto postulate at a time even through explicit social welfare functions.
    Metroeconomica 07/2013; 64(3). DOI:10.1111/meca.12012 · 0.65 Impact Factor
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    • "The extension to the case with a potentially infinite number of generations, however, is problematic for all the main approaches, and indeed impossibility results easily obtain, for there exists no social welfare ordering that satisfies the rather standard axioms of Anonymity and Strong Pareto (see [11]). A number of recent contributions (see among the others, [4], [1], [5], [7], [3] ) have provided characterisation results for social welfare relations by dropping the completeness axiom for social welfare orderings. In this tradition, this paper provides a new characterisation of the leximin social welfare relation, and new characterisations of the maximin and recursive maximin social welfare relations based on the Harm principle in the context of economies with an infinite number of agents. "
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    ABSTRACT: This paper analyses Rawls's celebrated difference principle, and a set of refinements of it, in societies with a finite and an infinite number of agents. First, a unified framework of analysis is provided, which allows one to characterise a family of egalitarian principles by means of a new axiom -the Harm Principle -recently proposed by [12]. This is quite interesting, because the Harm principle is meant to capture a liberal requirement of noninterference and it incorporates no obvious egalitarian content. Second, a complete axiomatic characterisation of a new social welfare function recently proposed by John Roemer [16], [17] -the recursive maximin -is provided. Finally, a set of new char-acterisations of refinements of the difference principle (the leximin and the recursive maximin) in the intergenerational context with an infinite number of agents is derived. JEL classification. D63 (Equity, Justice, Inequality, and Other Norma-tive Criteria and Measurement); D70 (Analysis of Collective Decision-Making); Q01 (Sustainable development).
    SSRN Electronic Journal 05/2013; DOI:10.2139/ssrn.1440194
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