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Social Choice and Welfare

, Volume 12, Issue 3, pp 233–244 | Cite as

Essentially lexicographic aggregation

  • Ulrich Krause
Article

Abstract

In the paper a new approach to lexicography is developed by which in the general framework of ordered blocks with a monotonic basis it is shown that a nontrivial ordering is translation-invariant if and only if it is essentially lexicographic of degree n. Here, the latter means that the ordering can be represented by an ordinary lexicographic ordering in n dimensions. As an application it is shown that a nontrivial social welfare ordering on Euclidean space possesses a useful invariance property (cardinality and non comparability) if and only if the ordering is essentially lexicographic of a strong kind in that it can be obtained from ordinary lexicography by permutation, cutting-off and order reversal with respect to components. This result generalizes the characterization of lexical individual dictatorship obtained by Gevers and d'Aspremont and it provides, within the social welfare approach, a strong version of Arrow's impossibility theorem by not invoking any Pareto principle at all.

Keywords

Social Welfare Euclidean Space General Framework Order Reversal Invariance Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Ulrich Krause
    • 1
  1. 1.Department of MathematicsUniversity of BremenBremenGermany

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