IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v65y2013i3p190-194.html
   My bibliography  Save this article

Collective approval

Author

Listed:
  • Duddy, Conal
  • Piggins, Ashley

Abstract

We consider the problem of aggregating individual approval ballots into one collective approval ballot. An approval ballot is simply a subset of a given set of alternatives. An individual may approve of as many alternatives as he or she wishes. Each approval is counted as a vote. We show that if an aggregation rule is neutral, consistent and discerning, then an alternative is collectively approved of if it receives a number of votes greater than the mean number of votes received by the alternatives and is not approved of if it receives a number of votes less than the mean.

Suggested Citation

  • Duddy, Conal & Piggins, Ashley, 2013. "Collective approval," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 190-194.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:3:p:190-194
    DOI: 10.1016/j.mathsocsci.2012.12.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489612001175
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2012.12.004?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. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
    2. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 621-625, December.
    3. B. Fine & K. Fine, 1974. "Social Choice and Individual Rankings II," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(4), pages 459-475.
    4. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    5. B. Fine & K. Fine, 1974. "Social Choice and Individual Ranking I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(3), pages 303-322.
    6. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    7. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    8. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, 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. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    2. 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.
    3. Trevor Leach & Robert C. Powers, 2020. "Majority rule on j-rich ballot spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 639-655, 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. 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.
    2. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    3. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    4. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
    5. Trevor Leach & Robert C. Powers, 2020. "Majority rule on j-rich ballot spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 639-655, April.
    6. François Maniquet & Philippe Mongin, 2015. "Approval voting and Arrow’s impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 519-532, March.
    7. Martínez, Ricardo & Moreno, Bernardo, 2017. "Qualified voting systems," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 49-54.
    8. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    9. Norihisa Sato, 2014. "A characterization result for approval voting with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 809-825, December.
    10. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    11. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.
    12. Burka, David & Puppe, Clemens & Szepesvary, Laszlo & Tasnadi, Attila, 2016. "Neural networks would 'vote' according to Borda's rule," Working Paper Series in Economics 96, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    13. José Alcantud & Annick Laruelle, 2014. "Dis&approval voting: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 1-10, June.
    14. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    15. Barberà, Salvador & Bossert, Walter & Moreno-Ternero, Juan D., 2023. "Wine rankings and the Borda method," Journal of Wine Economics, Cambridge University Press, vol. 18(2), pages 122-138, May.
    16. Antonin Macé, 2017. "Voting with evaluations: characterizations of evaluative voting and range voting," Working Papers halshs-01222200, HAL.
    17. Jordi Massó & Marc Vorsatz, 2008. "Weighted approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 129-146, July.
    18. Alcantud, José Carlos R. & de Andres Calle, Rocio & Cascon, José Manuel, 2012. "Approval consensus measures," MPRA Paper 39610, University Library of Munich, Germany.
    19. 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.
    20. 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.

    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:65:y:2013:i:3:p:190-194. 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.