Skip to main content
Log in

Voting power when using preference ballots

  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

In this paper we provide a generalized power index which gives a measurement of voting power in multi-candidate elections with weighted voting using preference ballots. We use the power index to compare the power of various players between an election using plurality and one using the Borda method. The power index is based upon the Banzhaf power index.

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.

Similar content being viewed by others

References

  1. Banzhaf JF III (1965) Weighted voting doesn't work: A mathematical analysis. Rutgers Law Rev 19: 317–343

    Google Scholar 

  2. Bolger EM (1983) The Banzhaf index for multicandidate presidential elections. SIAM J Algebraic Discrete Methods 4: 422–458

    Google Scholar 

  3. Bolger EM (1986) Power indices for multicandidate voting games. Int J Game Theory 14: 175–186

    Google Scholar 

  4. Bolger EM (1990) A characterization of an extension of the Banzhaf value to multicandidate voting games. SIAM J Discrete Math 3(4): 466–477

    Google Scholar 

  5. Cayley A (1891) On the analytical forms called trees. Collected Mathematical Papers, Cambridge University Press, Cambridge 4: 112–115

    Google Scholar 

  6. Even S (1973) Algorithmic Combinatorics. MacMillan, New York

    Google Scholar 

  7. Feld SL, Grofman B (1990) A theorem connecting Shapley-Owen power scores and the radius of the yolk in two dimensions. Soc Choice Welfare 7: 71–74

    Google Scholar 

  8. Gross OA (1962) Preferential arrangements. Amer Math Monthly 69: 4–8

    Google Scholar 

  9. MacMahon PA (1891) Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. Proc London Math Soc 22: 330–346

    Google Scholar 

  10. Mor M, Fraenkel AS (1984) Cayley Permutations. Discrete Math 48: 101–112

    Google Scholar 

  11. Motzkin TS (1971) Sorting numbers for cylinders and other classification numbers. Proc Symp Pure Math Amer Math Soc, Providence, RI, pp 167–176

  12. Rae DW (1969) Decision rules and individual values in constitutional choice. Amer Polit Science Rev 63: 40–56

    Google Scholar 

  13. Saari DG (1994) Geometry of Voting. Springer, Berlin (1994)

    Google Scholar 

  14. Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. Amer Pol Sci Rev 48: 787–792

    Google Scholar 

  15. Straffin PD (1989) Spatial models of power and voting outcomes. In: Roberts F (ed.) Applications of combinatorics and graph theory to the biological and social sciences. Springer, Berlin pp 315–335

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haunsperger, D.B., Melville, D.J. Voting power when using preference ballots. Soc Choice Welfare 13, 457–465 (1996). https://doi.org/10.1007/BF00182856

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00182856

Keywords

Navigation