In this article, we analyse the possibility of extending the Moulin theorem to Condorcet voting correspondences. Moulin (1988) established that every Condorcet voting function suffers from the No Show Paradox, or Abstention Paradox, which means that in some voting situations some voters would achieve a better result by abstaining (in other words, could manipulate the election by abstaining). This problem is similar to that of extending the Gibbard–Satterthwaite theorem on voting manipulation through casting an insincere ballot to voting correspondences. The main result of the paper states that for every Condorcet voting correspondence there are situations in which every optimistic or pessimistic voter with some preferences could manipulate the election by abstaining. Another result states, by counterexample, that some Condorcet voting correspondences are free from the Abstention Paradox from the point of view of other types of voters.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Barberá S, Dutta B, Sen AK (2001) Strategy-proof social choice correspondences. J Econ Theory 101: 374–394
Ching S, Zhou L (2002) Multi-valued strategy-proof social choice rules. Soc Choice Welf 19: 569–580
Duggan J, Schwartz T (2000) Strategic manipulability without resoluteness or shared beliefs: Gibbard–Satterthwaite generalized. Soc Choice Welf 17: 85–93
Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33: 469–489
Fishburn PC, Brams SJ (1983) Paradoxes of preferential voting. Math Mag 56: 207–214
Gärdenfors P (1976) Manipulation of social choice functions. J Econ Theory 13: 217–228
Jimeno JL (2003) Propiedades de Participación en los métodos de agregación de preferencias. PhD thesis, Universidad de Alcalá, Madrid, España
Jimeno JL, Pérez J, García E (2003) Some results concerning No Show Paradoxes. XXVIII Simposio de Análisis Económico, Sevilla, España
Moulin H (1988) Condorcet’s Principle implies the No Show Paradox. J Econ Theory 45: 53–64
Pérez J (1995) Incidence of no-show paradoxes in Condorcet choice functions. Invest Econ XIX 1(1): 139–154
Pérez J (2001) The strong No Show Paradoxes are a common flaw in Condorcet voting correspondences. Soc Choice Welf 18: 601–616
Taylor AD (2002) The manipulability of voting systems. Am Math Mon 109: 321–337
Taylor AD (2005) Social choice and the mathematics of manipulation. Cambridge University Press
Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9: 43–52
Young HP, Levenglick A (1978) A consistent extension of Condorcet election principle. SIAM J Appl Math 35: 285–300
Rights and permissions
About this article
Cite this article
Jimeno, J.L., Pérez, J. & García, E. An extension of the Moulin No Show Paradox for voting correspondences. Soc Choice Welf 33, 343–359 (2009). https://doi.org/10.1007/s00355-008-0360-6
- Utility Function
- Linear Order
- Social Choice Function
- Vote Situation
- Extension Order