Skip to main content
Log in

Strategic manipulability of self-selective social choice rules

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We provide exact relations giving the probability of individual and coalitional manipulation of three specific social choice functions (Borda rule, Copeland rule, Plurality rule) in three-alternative elections when the notion of self-selectivity is imposed. We use each type of tie-breaking rule in the case of three-candidate election in order to make the results more robust. Analyzing our probabilities, we can point out that the probability of individual and coalitional manipulation tend to vanish significantly when the notion of self-selectivity is imposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Aleskerov, F., & Kurbanov, E. (1999). degree of manipulability of social choice procedures. In Alkan, et al. (Eds.), Current trends in economics (pp. 13–28). Berlin Heidelberg New York: Springer.

    Chapter  Google Scholar 

  • Barberà, S., & Beviá, S. (2002). Self-selection consistent functions. Journal of Economic Theory, 105, 263–277.

    Article  Google Scholar 

  • Barberà, S., & Jackson, M. O. (2004). Choosing how to choose: Self-stable majority rules and constitutions. The Quarterly Journal of Economics, 119(3), 1011–1048.

    Article  Google Scholar 

  • Diss, M., Louichi, A., Merlin, V., & Smaoui, H. (2012). An example of probability computations under the IAC assumption: The stability of scoring rules. Mathematical Social Sciences, 64(1), 57–66.

    Article  Google Scholar 

  • Diss, M., & Merlin, V. (2010). On the stability of a triplet of scoring rules. Theory and Decision, 69, 289–316.

    Article  Google Scholar 

  • Ehrhart, E. (1962). Sur les polyèdres rationnels homothétiques à n dimensions. Comptes rendus de l’Académie des sciences Paris, 254, 616–618.

    Google Scholar 

  • Ehrhart, E. (1967). Sur un problème de géométrie diophantienne linéaire. Ph.D. thesis, J R A Math, vol. 226, pp. 1–49 .

  • Favardin, P., & Lepelley, D. (2006). Some further results on the manipulability of social choice rules. Social Choice and Welfare, 26, 485–509.

    Article  Google Scholar 

  • Favardin, P., Lepelley, D., & Serais, J. (2002). Borda rule, Copeland method and strategic manipulation. Review of Economic Design, 7, 213–228.

    Article  Google Scholar 

  • Gehrlein, W. V., & Fishburn, P. C. (1976). Condorcet’s paradox and anonymous preference profiles. Public Choice, 26, 1–18.

    Article  Google Scholar 

  • Gehrlein, W. V., & Lepelley, D. (2003). On some limitations of the median voting rule. Public Choice, 117, 177–190.

    Article  Google Scholar 

  • Gibbard, A. F. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–601.

    Article  Google Scholar 

  • Guilbaud, G. T. (1952). Les théories de l’intérêt général et le problème logique de l’agrégation. Economie Appliquée, 5, 501–584.

    Google Scholar 

  • Houy, N. (2003). Dynamics of stable sets of constitutions. Mimeo.

  • Houy, N. (2004). A note on the impossibility of a set of constitutions stable at different levels. Mimeo.

  • Houy, N. (2005). De la stabilité des procédures et constitutions en théorie du choix social. Ph.D. Thesis, Paris 1.

  • Kelly, J. (1988). Minimal manipulability and local strategy-proofness. Social Choice and Welfare, 5, 81–85.

    Article  Google Scholar 

  • Kelly, J. (1993). Almost all social choice rules are highly manipulable, but few aren’t. Social Choice and Welfare, 10, 161–175.

    Article  Google Scholar 

  • Koray, S. (2000). Self-selective social choice functions verify Arrow and Gibbard–Satterthwaite theorems. Econometrica, 68(4), 981–995.

    Article  Google Scholar 

  • Koray, S., & Unel, B. (2003). Charactrization of self-selective social choice functions on the tops-only domain. Social Choice and Welfare, 20, 495–507.

    Article  Google Scholar 

  • Laslier, J.-F. (2010). In silico voting experiments. In J.-F. Laslier & R. Sanver (Eds.), Handbook of approval voting (pp. 311–335). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Lepelley, D., Louichi, A., & Smaoui, H. (2008). On Ehrhart polynomials and probability calculations in voting theory. Social Choice and Welfare, 30, 363–383.

    Article  Google Scholar 

  • Lepelley, D., & Mbih, B. (1987). The proportion of coalitionally unstable situations under the plurality rule. Economics Letters, 24, 311–315.

    Article  Google Scholar 

  • Lepelley, D., & Mbih, B. (1994). The vulnerability of four social choice rules to coalitional manipulation of preferences. Social Choice and Welfare, 11, 253–265.

    Article  Google Scholar 

  • Lepelley, D., & Mbih, B. (1996). Strategic manipulation in committees using the plurality rule: Alternative concepts and frequency calculations. Group Decision and Negotiation, 6, 119–138.

    Article  Google Scholar 

  • Lepelley, D., & Valognes, F. (2003). Voting rules, manipulability and social homogeneity. Public Choice, 116, 165–184.

    Article  Google Scholar 

  • Maus, S., Peters, H., & Storcken, T. (2007). Minimal manipulability: Anonymity and unanimity. Social Choice and Welfare, 29, 247–269.

    Article  Google Scholar 

  • Nitzan, S. (1985). The vulnerability of point-voting schemes to preference variation and strategic manipulation. Public Choice, 47, 349–370.

    Article  Google Scholar 

  • Satterthwaite, M. A. (1975). Strategyproofness and Arrow’s conditions: Existence and correspondences for voting procedures and social welfare functions. Journal of Economic Theory, 10, 187–217.

    Article  Google Scholar 

  • Serais, J. Sensivity to strategic candidacy by exiting for scoring rules and Copeland. University of Caen Basse-Normandie, unpublished paper.

  • Smith, D. (1999). Manipulability measures of common social choice functions. Social Choice and Welfare, 16, 639–661.

    Article  Google Scholar 

  • Verdoolaege, S., Seghir, R., Beyls, K., Loechner, V., & Bruynooghe, M. (2004). Analytical computation of Ehrhart polynomials: Enabling more compiler analysis and optimizations. In Proceedings of international conference on compilers, architecture, and synthesis for embedded systems. Washington DC, pp. 248–258.

  • Wilson, M. C., & Pritchard, G. (2007). Probability calculations under the IAC hypothesis. Mathematical Social Sciences, 54, 244–256.

    Article  Google Scholar 

Download references

Acknowledgments

I am indebted to Richard Baron, Gérald Chatagnon, Ahmad Fliti and two anonymous referees of this journal for helpful comments on an earlier version of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mostapha Diss.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Diss, M. Strategic manipulability of self-selective social choice rules. Ann Oper Res 229, 347–376 (2015). https://doi.org/10.1007/s10479-014-1763-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-014-1763-7

Keywords

JEL Classification

Navigation