Fixed‐step anonymous overtaking and catching‐up

Abstract

We investigate criteria for evaluating infinite utility streams that satisfy fixed‐step anonymity and include some notion of overtaking or catching‐up. We do so in a generalized setting that does not require us to specify the underlying finite‐dimensional criterion (e.g. utilitarianism or leximin). We present axiomatizations that rely on weaker axioms than those in the literature, and which in one case is new. We also provide a complete analysis of the relationships between the symmetric parts of these criteria and likewise for the asymmetric parts.

The Limit of Discounted Utilitarianism

“…Two examples of such extended anonymity axioms that are compatible with SP are Lauwers's [22] FixedStep Anonymity (see e.g. Fleurbaey and Michel [14], Asheim and Banerjee [2], Sakai [26], Kamaga and Kojima [19]) and the Strong Relative Anonymity axiom in Asheim et al [3]. As exemplified by these conditions, imposing invariance under infinite permutations is a risky business, and may come at the cost of Koopmans's [20] Stationarity axiom.…”

Intergenerational Equity

“…T 0 : It follows from the results ofAsheim & Tungodden (2004),Basu & Mitra (2007b), andAsheim & Banerjee (2010) that the SWRs ≿ o U , ≿ o L , ≿ c U , and ≿ c L can be characterized by adding one of the following two axioms.…”

Equitable intergenerational preferences and sustainability

“…There is a series of contributions (e.g., Lauwers, 1997;Fleurbaey & Michel, 2003;Asheim & Tungodden, 2004;Banerjee, 2006;Kamaga & Kojima 2009, 2010Asheim & Banerjee, 2010) that investigate how more comparability can be achieved by adding additional axioms, keeping in mind that the Lauwers-Zame impossibility result rules out completeness of any explicitly defined SWR. These versions of undiscounted utilitarianism and leximin invoke overtaking and catching-up procedures which are beyond the scope of the current chapter.…”