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Approval voting and arrow's impossibility theorem

  • Mongin, Philippe

    ()

    (HEC Paris)

  • Maniquet, François

Author's abstract. Approval voting has attracted considerable interest among voting theorists, but they have rarely investigated it in the Arrovian frame-work of social welfare functions (SWF) and never connected it with Arrow’s impossibility theorem. This note explores these two direc- tions. Assuming that voters have dichotomous preferences, it first characterizes approval voting in terms of its SWF properties and then shows that these properties are incompatible if the social preference is also taken to be dichotomous. The positive result improves on some existing characterizations of approval voting in the literature, as well as on Arrow’s and May’s classic analyses of voting on two alternatives. The negative result corresponds to a novel and perhaps surprising version of Arrow’s impossibility theorem.

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Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 954.

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Length: 16 pages
Date of creation: 17 Nov 2011
Date of revision:
Handle: RePEc:ebg:heccah:0954
Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
Web page: http://www.hec.fr/

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  1. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  2. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer, vol. 31(1), pages 151-162, June.
  3. Campbell, Donald E. & Kelly, Jerry S., 2000. "Weak independence and veto power," Economics Letters, Elsevier, vol. 66(2), pages 183-189, February.
  4. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer, vol. 28(1), pages 127-141, January.
  5. Brams, S.J. & Fishburn, P.C., 2003. "Going from Theory to Practice: The Mixed Success of Approval Voting," Working Papers 03-06, C.V. Starr Center for Applied Economics, New York University.
  6. Gaertner, Wulf, 2002. "Domain restrictions," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 3, pages 131-170 Elsevier.
  7. Ju, Biung-Ghi, 2011. "Collectively rational voting rules for simple preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 143-149, March.
  8. Baigent, Nick & Xu, Yongsheng, 1991. "Independent necessary and sufficient conditions for approval voting," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 21-29, February.
  9. Norihisa Sato, 2014. "A characterization result for approval voting with a variable set of alternatives," Social Choice and Welfare, Springer, vol. 43(4), pages 809-825, December.
  10. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer, vol. 27(3), pages 621-625, December.
  11. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
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