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Liberal approaches to ranking infinite utility streams: When can we avoid interferences?

Alcantud, José Carlos R. (2011): Liberal approaches to ranking infinite utility streams: When can we avoid interferences?

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In this work we analyse social welfare relations on sets of infinite utility streams that verify various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that agree with axioms of that kind together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if weak Pareto optimality is imposed. We first prove that extending the horizon to infinity produces a reversal of such impossibility result. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between continuity and non-interference principles, both under ordinal and cardinal views of the problem. Our analysis ends with some insights on the property of representability in the presence of non-interference assumptions. In particular we prove that all social welfare functions that verify a very mild efficiency property must exert some interference (penalising both adverse and favorable changes) on the affairs of particular generations.

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