The impossibility of social evaluations of infinite streams with strict inequality aversion
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The impossibility of social evaluations of infinite streams with strict inequality aversion José Carlos R. Alcantud
Received: 11 March 2013 / Accepted: 13 March 2013 © SAET 2013
Abstract We are concerned with the problem of aggregating infinite utility streams and the possible adoption of consequentialist equity principles. 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. We also prove that the Hara–Shinotsuka–Suzumura–Xu impossibility for semicontinuous social welfare relations remains under the latter distributional postulate. Keywords Social welfare function · Inequality aversion · Pigou–Dalton transfer principle · Monotonicity JEL Classification
D63 · D71 · D90
1 Introduction This paper is primarily concerned with the problem of aggregating infinite utility streams and the possible adoption of distributive equity principles. We prove that there is a fundamental incompatibility between salient postulates of strict inequality aversion like the Strong Equity Principle (Bossert et al. 2007), the Pigou–Dalton Transfer principle (Sakai 2006; Bossert et al. 2007), the Lorenz Domination principle
J. C. R. Alcantud (B) Campus Unamuno. Edificio FES, Universidad de Salamanca, 37007 Salamanca, Spain e-mail: [email protected] URL:http://diarium.usal.es/jcr
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J. C. R. Alcantud
(Hara et al. 2008), or Altruistic Equity (Hara et al. 2006; Sakamoto 2012), and the Basu–Mitra approach that uses social welfare functions (SWFs) and renounces continuity. If we abandon the use of utilities, we complement Sakai (2006) and Hara et al. (2008) to conclude that those postulates are incompatible with semicontinuous preferences too. As Sakai (2006) has put it, there are two ethical considerations that capture the concept of intergenerational equity: inequality aversion and equality in evaluating allocations. The latter is in the utilitarian tradition à-la-Sidgwick and Diamond, and requires that the welfare orderings should not be biased against any generation. In formal terms, it appeals to anonymity axioms that impose the impartial treatment of all generations. The former has received much attention in recent years. The aforementioned distributional axioms have been introduced in the literature on intergenerational justice to explore the implications of such ethical standpoint; thus, they have the common spirit of expressing a strict preference for distributions of utilities among generations that reduce inequality in various forms. Irrespective of the egalitarian position that is adopted, the essential shortfall of the approach by numerical evaluations or SWFs in this context has been brought to the fore by a number of contributions. Either, if one requests anonymity-type properties (Basu and Mitra 2003; Crespo et al. 2009), the very mild Ham
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