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Approval Voting on Dichotomous Preferences

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  • Marc Vorsatz

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Abstract

The aim of this paper is to find normative foundations of Approval Voting. In order to show that Approval Voting is the only social choice function that satisfies anonymity, neutrality, strategy-proofness and strict monotonicity we rely on an intermediate result which relates strategy-proofness of a social choice function to the properties of Independence of Irrelevant Alternatives and monotonicity of the corresponding social welfare function. Afterwards we characterize Approval Voting by means of strict symmetry, neutrality and strict monotonicity and relate this result to May's Theorem. Finally, we show that it is possible to substitute the property of strict monotonicity by the one efficiency of in the second characterization.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 28 (2007)
Issue (Month): 1 (January)
Pages: 127-141

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Handle: RePEc:spr:sochwe:v:28:y:2007:i:1:p:127-141

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  1. Steven Brams & Peter Fishburn, 2005. "Going from theory to practice: the mixed success of approval voting," Social Choice and Welfare, Springer, Springer, vol. 25(2), pages 457-474, December.
  2. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer, Springer, vol. 17(1), pages 85-93.
  3. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  4. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, Springer, vol. 19(3), pages 569-580.
  5. Blair, Douglas & Muller, Eitan, 1983. "Essential aggregation procedures on restricted domains of preferences," Journal of Economic Theory, Elsevier, vol. 30(1), pages 34-53, June.
  6. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer, Springer, vol. 31(1), pages 151-162, June.
  7. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, Econometric Society, vol. 45(1), pages 53-89, January.
  8. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
  9. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 509-19, March.
  10. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Theodore Groves & Martin Loeb, 1974. "Incentives and Public Inputs," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 29, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  13. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  14. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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Citations

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Cited by:
  1. Massó, Jordi & Vorsatz, Marc, 2006. "Weighted Approval Voting," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Jorge Alcalde-Unzu & Marc Vorsat, 2011. "Non-anonymous ballot aggregation: an axiomatic generalization of Approval Voting," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra, Departamento de Economía - Universidad Pública de Navarra 1103, Departamento de Economía - Universidad Pública de Navarra.
  3. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
  4. Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-15, Indian Statistical Institute, New Delhi, India.
  5. Mongin, Philippe & Maniquet, François, 2011. "Approval voting and arrow's impossibility theorem," Les Cahiers de Recherche 954, HEC Paris.
  6. Rosa Camps & Xavier Mora & Laia Saumell, 2013. "A continuous rating method for preferential voting. The incomplete case," Social Choice and Welfare, Springer, Springer, vol. 40(4), pages 1111-1142, April.
  7. Alcantud, José Carlos R. & de Andres Calle, Rocio & Cascon, José Manuel, 2012. "Approval consensus measures," MPRA Paper 39610, University Library of Munich, Germany.
  8. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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