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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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File URL: http://hdl.handle.net/10.1007/s00355-006-0149-4
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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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References

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  1. Groves, Theodore & Loeb, Martin, 1975. "Incentives and public inputs," Journal of Public Economics, Elsevier, vol. 4(3), pages 211-226, August.
  2. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer, vol. 17(1), pages 85-93.
  3. 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.
  4. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  5. 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).
  6. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  7. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  8. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
  9. Marc Vorsatz, 2004. "Scoring Rules on Dichotomous Preferences," UFAE and IAE Working Papers 617.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  10. 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.
  11. Steven Brams & Peter Fishburn, 2005. "Going from theory to practice: the mixed success of approval voting," Social Choice and Welfare, Springer, vol. 25(2), pages 457-474, December.
  12. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  13. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
  14. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
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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. Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
  3. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2007. "Size Approval Voting," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
  5. 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).
  6. Rosa Camps & Xavier Mora & Laia Saumell, 2013. "A continuous rating method for preferential voting. The incomplete case," Social Choice and Welfare, Springer, vol. 40(4), pages 1111-1142, April.
  7. Mongin, Philippe & Maniquet, François, 2011. "Approval voting and arrow's impossibility theorem," Les Cahiers de Recherche 954, HEC Paris.
  8. Alcantud, José Carlos R. & de Andres Calle, Rocio & Cascon, José Manuel, 2012. "Approval consensus measures," MPRA Paper 39610, University Library of Munich, Germany.

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