David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Theory and Decision 52 (3):287-301 (2002)
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 â a situation called intradimensional single-peakedness â 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
|Keywords||Arrow's theorem single-peakedness multidimensional preference orderings|
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