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The proximity condition

  • Conal Duddy

    ()

  • Ashley Piggins

    ()

We investigate the social choice implications of what we call “the proximity condition”. Loosely speaking, this condition says that whenever a profile moves “closer” to some individual’s point of view, then the social choice cannot move “further away” from this individual’s point of view. We apply this idea in two settings: merging functions and preference aggregation. The precise formulation of the proximity condition depends on the setting. First, restricting attention to merging functions that are interval scale invariant, we prove that the only functions that satisfy proximity are dictatorships. Second, we prove that the only social welfare functions that satisfy proximity and a version of the Pareto criterion are dictatorships. We conclude that either proximity is not an attractive normative requirement after all, or we must give up some other social choice condition. Another possibility is that our normative intuition about proximity needs to be codified using different axioms. Copyright Springer-Verlag 2012

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File URL: http://hdl.handle.net/10.1007/s00355-011-0630-6
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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 39 (2012)
Issue (Month): 2 (July)
Pages: 353-369

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Handle: RePEc:spr:sochwe:v:39:y:2012:i:2:p:353-369
DOI: 10.1007/s00355-011-0630-6
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  1. Aczel, Janos & Roberts, Fred S., 1989. "On the possible merging functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 205-243, June.
  2. Juan Perote-Peña & Ashley Piggins, 2002. "Geometry and impossibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 831-836.
  3. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 102(1), pages 161-169.
  4. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2011. "Arrow’s theorem and max-star transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(1), pages 25-34, January.
  5. Quesada, Antonio, 2007. "Merging discrete evaluations," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 25-34, July.
  6. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
  7. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
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