Skip to main content
SpringerLink
Log in

A note on hierarchies in weighted voting games and partitions

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

Weighted voting games (WVGs) model situations where voters, possibly controlling different numbers of votes, vote yes or no on a proposition. A proposition passes if and only if the number of yes votes meets or exceeds a quota \(q\). Each winning coalition is a partition of an integer greater than or equal to \(q\), with parts taken from the set of all weights for that game. Results about WVGs are here interpreted as results about partitions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Armstrong, S., Friedman, J., Parker, C., Riethmiller, D., Watson, D.: Impossible hierarchies with respect to the Deegan–Packel power index (in preparation)

  2. Bean, D., Friedman, J., Parker, C.: Simple majority achievable hierarchies. Theory Decis. 65, 285–302 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Diffo Lambo, L., Moulen, J.: Ordinal equivalence of power notions in voting games. Theory Decis. 53, 313–325 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Friedman, J., McGrath, L., Parker, : Achievable hierarchies in voting games. Theory Decis. 61, 305–318 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Isbell, J.: A class of simple games. Duke J. Math. 75, 423–439 (1975)

    MathSciNet  MATH  Google Scholar 

  6. Taylor, A.D., Zwicker, W.S.: Simple Games: Desirability Relations, Trading, Pseudoweightings. Princeton University Press, Princeton (1999)

    MATH  Google Scholar 

  7. Tomiyama, Y.: Simple game, voting representation and ordinal power equivalence. Int. J. Policy Inf. 11, 67–75 (1987)

    Google Scholar 

Download references

Acknowledgments

I would like to thank the editors of the journal for providing this opportunity to honor Marvin Knopp. I would also like to thank the anonymous referee for suggestions that clarified and much improved this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, 5998 Alcalá Park, University of San Diego, San Diego, CA, 92110, USA

    Jane Friedman

Authors
  1. Jane Friedman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jane Friedman.

Additional information

This work is dedicated with love and respect to the memory of Marvin Knopp, whose support and encouragement have been essential to my career and my life.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Friedman, J. A note on hierarchies in weighted voting games and partitions. Ramanujan J 41, 305–310 (2016). https://doi.org/10.1007/s11139-015-9686-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11139-015-9686-8

Keywords

Mathematics Subject Classification

Search

Navigation