IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v42y2014i4p913-926.html
   My bibliography  Save this article

A Borda count for partially ordered ballots

Author

Listed:
  • John Cullinan
  • Samuel Hsiao
  • David Polett

Abstract

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • John Cullinan & Samuel Hsiao & David Polett, 2014. "A Borda count for partially ordered ballots," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 913-926, April.
    • Handle: RePEc:spr:sochwe:v:42:y:2014:i:4:p:913-926
    DOI: 10.1007/s00355-013-0751-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-013-0751-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-013-0751-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Niemi, Richard G., 1984. "The Problem of Strategic Behavior under Approval Voting," American Political Science Review, Cambridge University Press, vol. 78(4), pages 952-958, December.
    2. Ferejohn, John A. & Fishburn, Peter C., 1979. "Representations of binary decision rules by generalized decisiveness structures," Journal of Economic Theory, Elsevier, vol. 21(1), pages 28-45, August.
    3. Brown, Donald J., 1974. "An approximate solution to Arrow's problem," Journal of Economic Theory, Elsevier, vol. 9(4), pages 375-383, December.
    4. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    5. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    6. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328-328.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    2. Nehring, Klaus & Puppe, Clemens, 2019. "Resource allocation by frugal majority rule," Working Paper Series in Economics 131, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    3. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.
    4. Nehring, Klaus & Puppe, Clemens, 2022. "Condorcet solutions in frugal models of budget allocation," Working Paper Series in Economics 156, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    5. Ivanov, Asen, 2022. "The Borda count with weak preferences," Economics Letters, Elsevier, vol. 210(C).
    6. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.
    7. Wen Li & Yicheng Ye & Nanyan Hu & Xianhua Wang & Qihu Wang, 2019. "Real-Time Warning and Risk Assessment of Tailings Dam Disaster Status Based on Dynamic Hierarchy-Grey Relation Analysis," Complexity, Hindawi, vol. 2019, pages 1-14, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sholomov, Lev A., 2000. "Explicit form of neutral social decision rules for basic rationality conditions," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 81-107, January.
    2. Susumu Cato, 2015. "Conditions on social-preference cycles," Theory and Decision, Springer, vol. 79(1), pages 1-13, July.
    3. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    4. Jun Iritani & Tomoyuki Kamo & Ryo-ichi Nagahisa, 2013. "Vetoer and tie-making group theorems for indifference-transitive aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 155-171, January.
    5. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    6. Elizabeth Maggie Penn, 2015. "Arrow’s Theorem and its descendants," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 14, pages 237-262, Edward Elgar Publishing.
    7. Truchon M., 1996. "Voting games and acyclic collective choice rules," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 55-55, February.
    8. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    9. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
    10. Lahiri, Somdeb, 2009. "A sufficient condition for acyclic social choice in a single-profile world," MPRA Paper 14129, University Library of Munich, Germany.
    11. László Csató, 2018. "Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom," Group Decision and Negotiation, Springer, vol. 27(6), pages 1011-1027, December.
    12. Marcel Richter & Kam-Chau Wong, 2008. "Preference densities and social choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 225-238, August.
    13. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    14. Michel Regenwetter & Bernard Grofman, 1998. "Approval Voting, Borda Winners, and Condorcet Winners: Evidence from Seven Elections," Management Science, INFORMS, vol. 44(4), pages 520-533, April.
    15. Csaba, László, 2014. "Átmenettan és közgazdaságtan. Módszertani tanulságok egy részterület műveléséből [Transitology" and economics. Methodological lessons to be drawn from work in a partial territory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 53-67.
    16. Crispin H. V. Cooper, 2020. "Quantitative Models of Well-Being to Inform Policy: Problems and Opportunities," Sustainability, MDPI, vol. 12(8), pages 1-13, April.
    17. Bock, Hans-Hermann & Day, William H. E. & McMorris, F. R., 1998. "Consensus rules for committee elections," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 219-232, May.
    18. Kotaro Suzumura, 2020. "Reflections on Arrow’s research program of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 219-235, March.
    19. Leo Katz & Alvaro Sandroni, 2020. "Limits on power and rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 507-521, March.
    20. Le Breton, Michel & Truchon, Michel, 1997. "A Borda measure for social choice functions," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 249-272, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:42:y:2014:i:4:p:913-926. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.