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Intradimensional single-peakedness and the multidimensional Arrow problem

List, Christian (2002) Intradimensional single-peakedness and the multidimensional Arrow problem. Theory and Decision, 52 (3). pp. 287-301. ISSN 1573-7187

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Identification Number: 10.1023/A:1019620322895


Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance of a single dimension. In particular, even if preferences are single-peaked across individuals within each dimension -- a situation called intradimensional single-peakedness -- any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed.

Item Type: Article
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Additional Information: Published 2002 © Springer Netherlands. The original publication is available at LSE has developed LSE Research Online so that users may access research output of the School. Copyright and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (<>) of the LSE Research Online website.
Divisions: Government
Philosophy, Logic and Scientific Method
Subjects: H Social Sciences > H Social Sciences (General)
Date Deposited: 31 Mar 2006
Last Modified: 20 Apr 2021 00:43

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