Continuity and egalitarianism in the evaluation of infinite utility streams

Abstract

There exists a utilitarian traditionà la Sidgwick of treating equal generations equally. Diamond showed that there exists no social evaluation ordering over infinite utility streams in the presence of the Pareto principle, the Sidgwick principle, and continuity. Instead of requiring the Sidgwick principle of procedural fairness, we focus on two principles of distributional egalitarianism along the line of the Pigou-Dalton transfer principle and the Lorenz domination principle, and show that there exists no social evaluation relation satisfying one of these egalitarian principles and the weakened continuity and rationality axioms even in the absence of the Pareto principle.

Sustainable recursive social welfare functions

“…Such equity conditions have been used in the setting of infinite streams by, e.g., Birchenhall and Grout (1979), Asheim (1991), Fleurbaey and Michel (2001), and Hara et al (2008). Note that condition HEF involves a comparison between a sacrifice by a single generation and a uniform gain for each member of an infinite set of generations that are worse-off.…”

Multi-profile intergenerational social choice

“…Among many contributions that appeared after Diamond (1965), those which are most relevant in the present context include Asheim, Mitra and Tungodden (2007), Basu and Mitra (2003;, Bossert, Sprumont and Suzumura (2007), Hara, Shinotsuka, Suzumura and Xu (2007) and Svensson (1980). Although these two lines of inquiry are related in the sense that both are concerned with aggregating generational evaluations of their well-beings into the overall social evaluation, they contrast sharply in at least two respects.…”

Infinite-horizon choice functions

“…Diamond (1965) goes on to show that strong Pareto, finite anonymity and a continuity requirement are incompatible if the social relation is required to be transitive and complete. Instead of requiring the Sidgwickean principle of finite anonymity, Hara, Shinotsuka, Suzumura and Xu (2007) focus on two principles of distributional egalitarianism along the line of the Pigou-Dalton transfer principle and the Lorenz domination principle, and show that there exists no social evaluation relation satisfying one of these egalitarian principles and a weakened continuity condition even in the absence of the Pareto principle and completeness. Basu and Mitra (2003) show that strong Pareto, finite anonymity and representability by a real-valued function are incompatible.…”

“…We provide characterizations of all infinite-horizon choice functions satisfying either of the two axioms and, moreover, identify all choice functions with both properties. We then consider equity properties that are choice-theoretic versions of the Suppes-Sen principle, the Pigou-Dalton transfer principle and resource monotonicity (see Asheim, Mitra and Tungodden, 2007;Bossert, Sprumont and Suzumura, 2007;Hara, Shinotsuka, Suzumura and Xu, 2007, for equity properties imposed on rankings of infinite streams). Again, classes of infinite-horizon choice functions possessing one of these properties are characterized, and further axiomatizations are obtained by adding efficiency or time consistency.…”

“…For a recent vindication of this fact, see Bossert and Suzumura (2008). In the second place, a recent study by Hara, Shinotsuka, Suzumura and Xu (2007) shows that impossibility theorems persist in the context of evaluating infinite utility streams if only we retain weak vestiges of continuity, even when we dispose of completeness and coherence requirements on social evaluation relations altogether. may or may not be generated by a variety of optimality criteria.…”