IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v69y2014icp1-11.html
   My bibliography  Save this article

Unifying voting theory from Nakamura’s to Greenberg’s theorems

Author

Listed:
  • Saari, Donald G.

Abstract

Cycles, empty cores, intransitivities, and other complexities affect group decision and voting rules. Approaches that prevent these difficulties include the Nakamura number, Greenberg’s theorem, and single peaked preferences. The results derived here subsume and significantly extend these assertions while providing a common explanation for these seemingly dissimilar conclusions.

Suggested Citation

  • Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    • Handle: RePEc:eee:matsoc:v:69:y:2014:i:c:p:1-11
    DOI: 10.1016/j.mathsocsci.2014.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016548961400002X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2014.01.001?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. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, July.
    2. Donald G. Saari, 2009. "Condorcet Domains: A Geometric Perspective," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 161-182, Springer.
    3. Donald G. Saari, 2014. "A New Way to Analyze Paired Comparison Rules," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 647-655, August.
    4. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    5. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    6. Zwicker, William S., 1991. "The voters' paradox, spin, and the Borda count," Mathematical Social Sciences, Elsevier, vol. 22(3), pages 187-227, December.
    7. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    8. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, October.
    9. Tataru, Maria, 1999. "Growth rates in multidimensional spatial voting," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 253-263, May.
    10. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, October.
    11. Donald G. Saari, 1997. "The generic existence of a core for q -rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 219-260.
    12. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    13. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    14. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    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. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    2. Mathieu Martin & Zéphirin Nganmeni, 2019. "The fi nagle point might not be within the Ɛ-core: a contradiction with Bräuninger's result," THEMA Working Papers 2019-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Josep Freixas & Sascha Kurz, 2019. "Bounds for the Nakamura number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 607-634, April.
    4. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    5. McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.
    6. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2019. "Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk," THEMA Working Papers 2019-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    8. Donald G. Saari, 2019. "Arrow, and unexpected consequences of his theorem," Public Choice, Springer, vol. 179(1), pages 133-144, 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. Donald G. Saari, 2019. "Arrow, and unexpected consequences of his theorem," Public Choice, Springer, vol. 179(1), pages 133-144, April.
    2. Piggins, Ashley & Salerno, Gillian, 2016. "Sen cycles and externalities," Economics Letters, Elsevier, vol. 149(C), pages 25-27.
    3. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.
    4. A. J. McGann, 2004. "The Tyranny of the Supermajority," Journal of Theoretical Politics, , vol. 16(1), pages 53-77, January.
    5. Keith L. Dougherty & Julian Edward, 2022. "The effect of unconditional preferences on Sen’s paradox," Theory and Decision, Springer, vol. 93(3), pages 427-447, October.
    6. Lingfang (Ivy) Li & Donald Saari, 2008. "Sen’s theorem: geometric proof, new interpretations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 393-413, October.
    7. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    8. Saari, Donald G. & McIntee, Tomas J., 2013. "Connecting pairwise and positional election outcomes," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 140-151.
    9. Bargagliotti, Anna E. & Li, Lingfang (Ivy), 2009. "Decision Making Using Rating Systems: When Scale Meets Binary," MPRA Paper 16947, University Library of Munich, Germany.
    10. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    11. Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.
    12. Donald Saari, 2010. "Systematic analysis of multiple voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 217-247, February.
    13. Noriaki Okamoto & Toyotaka Sakai, 2019. "The Borda rule and the pairwise-majority-loser revisited," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 75-89, June.
    14. McIntee, Tomas J. & Saari, Donald G., 2017. "Likelihood of voting outcomes with generalized IAC probabilities," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 1-10.
    15. Ngoie, Ruffin-Benoit M., 2012. "Choix social et partage équitable : Une analyse mathématique a posteriori des élections législatives et présidentielles de 2006 et 2011 en RDC [Social choice and fair sharing: An a posteriori mathe," MPRA Paper 64915, University Library of Munich, Germany.
    16. Norman Schofield, 2013. "The “probability of a fit choice”," Review of Economic Design, Springer;Society for Economic Design, vol. 17(2), pages 129-150, June.
    17. Colander, David, 2009. "What Was “It” That Robbins Was Defining?," Journal of the History of Economic Thought, Cambridge University Press, vol. 31(4), pages 437-448, December.
    18. Antoinette Baujard, 2016. "Utilitarianism and anti-utilitarianism," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 40, pages 576-588, Edward Elgar Publishing.
    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. Bernholz, Peter, 1997. "Property rights, contracts, cyclical social preferences and the Coase theorem: A synthesis," European Journal of Political Economy, Elsevier, vol. 13(3), pages 419-442, September.

    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:eee:matsoc:v:69:y:2014:i:c:p:1-11. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.