Social Choice and Welfare

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

Essentially lexicographic aggregation

  • Ulrich Krause


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.


Social Welfare Euclidean Space General Framework Order Reversal Invariance Property 
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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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