IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v49y2017i3d10.1007_s00355-017-1066-4.html
   My bibliography  Save this article

The greatest unhappiness of the least number

Author

Listed:
  • Walter Bossert

    (Centre Interuniversitaire de Recherche en Economie Quantitative (CIREQ))

  • Kotaro Suzumura

    (Waseda University)

Abstract

We propose an alternative articulation of the Benthamite greatest-happiness-of-the-greatest-number principle. With ordinally measurable and interpersonally non-comparable utilities, the rule chooses those feasible alternatives that maximize the number of individuals who end up with their greatest element. This rule is tantamount to the plurality rule. Furthermore, in the spirit of Rawls’s maximin principle, we propose the greatest-unhappiness-of-the-least-number principle. In analogy to the greatest-happiness principle, the least-unhappiness principle is formally equivalent to the anti-plurality rule. Our main result is a characterization of the least-unhappiness principle.

Suggested Citation

  • Walter Bossert & Kotaro Suzumura, 2017. "The greatest unhappiness of the least number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 637-655, December.
    • Handle: RePEc:spr:sochwe:v:49:y:2017:i:3:d:10.1007_s00355-017-1066-4
    DOI: 10.1007/s00355-017-1066-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-017-1066-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-017-1066-4?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    2. Eyal Baharad & Shmuel Nitzan, 2005. "The inverse plurality rule—an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 173-178, October.
    3. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.
    4. Vincent Merlin, 2003. "The axiomatic characterization of majority voting and scoring rules," Post-Print halshs-00069506, HAL.
    5. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    7. Blackorby, Charles & Bossert, Walter & Donaldson, David, 2002. "Utilitarianism and the theory of justice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 11, pages 543-596, Elsevier.
    8. Barbera, Salvador & Dutta, Bhaskar, 1982. "Implementability via protective equilibria," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 49-65, June.
    9. Vincent Merlin & Jörg Naeve, 2000. "Implementation of Social Choice Functions via Demanding Equilibria," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 191/2000, Department of Economics, University of Hohenheim, Germany, revised 25 Sep 2001.
    10. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 575-583, March.
    11. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    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. 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.
    2. Kamaga, Kohei, 2018. "When do utilitarianism and egalitarianism agree on evaluation? An intersection approach," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 41-48.
    3. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    4. Salvatore Barbaro, 2024. "Electoral Methods and Political Polarization," Working Papers 2411, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    5. Jac C. Heckelman, 2023. "Negative voting social welfare functions: a characterization," Review of Economic Design, Springer;Society for Economic Design, vol. 27(1), pages 125-132, February.
    6. Kurihara, Takashi, 2018. "A simple characterization of the anti-plurality rule," Economics Letters, Elsevier, vol. 168(C), pages 110-111.
    7. Walter Bossert & Kotaro Suzumura, 2020. "Positionalist voting rules: a general definition and axiomatic characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 85-116, June.

    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. Hiroki Saitoh, 2022. "Characterization of tie-breaking plurality rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 139-173, July.
    2. Z. Emel Öztürk, 2020. "Consistency of scoring rules: a reinvestigation of composition-consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 801-831, September.
    3. Federico Fioravanti & Ulle Endriss, 2024. "Voting with Partial Orders: The Plurality and Anti-Plurality Classes," Papers 2404.17413, arXiv.org, revised Jun 2024.
    4. Z. Emel Ozturk, 2017. "A composition-consistency characterization of the plurality rule," Working Papers 2017_04, Business School - Economics, University of Glasgow.
    5. Kurihara, Takashi, 2018. "A simple characterization of the anti-plurality rule," Economics Letters, Elsevier, vol. 168(C), pages 110-111.
    6. Federico Fioravanti & Ulle Endriss, 2024. "Voting with Partial Orders: The Plurality and Anti-Plurality Classes," Working Papers 329, Red Nacional de Investigadores en Economía (RedNIE).
    7. Jac C. Heckelman, 2021. "Characterizing plurality using the majoritarian condition: a new proof and implications for other scoring rules," Public Choice, Springer, vol. 189(3), pages 335-346, December.
    8. Barberà, Salvador & Bossert, Walter, 2023. "Opinion aggregation: Borda and Condorcet revisited," Journal of Economic Theory, Elsevier, vol. 210(C).
    9. Wesley H. Holliday & Eric Pacuit, 2023. "An extension of May's Theorem to three alternatives: axiomatizing Minimax voting," Papers 2312.14256, arXiv.org, revised Jul 2024.
    10. Salvador Barberà & Walter Bossert & Kotaro Suzumura, 2021. "Daunou’s voting rule and the lexicographic assignment of priorities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 259-289, February.
    11. José García-Lapresta & A. Marley & Miguel Martínez-Panero, 2010. "Characterizing best–worst voting systems in the scoring context," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 487-496, March.
    12. Kurihara, Takashi, 2018. "Axiomatic characterisations of the basic best–worst rule," Economics Letters, Elsevier, vol. 172(C), pages 19-22.
    13. Kelly, Jerry S. & Qi, Shaofang, 2016. "Characterizing plurality rule on a fixed population," Economics Letters, Elsevier, vol. 146(C), pages 39-41.
    14. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    15. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    16. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    17. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    18. Fasil Alemante & Donald E. Campbell & Jerry S. Kelly, 2016. "Characterizing the resolute part of monotonic social choice correspondences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 765-783, October.
    19. Eliora Hout & Harrie Swart & Annemarie Veer, 2006. "Characteristic properties of list proportional representation systems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 459-475, December.
    20. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.

    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:49:y:2017:i:3:d:10.1007_s00355-017-1066-4. 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.