IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v57y2021i3d10.1007_s00355-021-01327-w.html
   My bibliography  Save this article

An Arrovian impossibility in combining ranking and evaluation

Author

Listed:
  • Justin Kruger

    (Université Paris-Dauphine, Université PSL, CNRS, LAMSADE)

  • M. Remzi Sanver

    (Université Paris-Dauphine, Université PSL, CNRS, LAMSADE)

Abstract

In a world where voters not only rank the alternatives but also qualify them as “approved” or “disapproved”, we observe that majoritarianism in preferences and majoritarianism in approvals are logically incompatible. We show that this observation generalises to the following result: every aggregation rule that respects unanimity and decomposes the aggregation of preferences and approvals is dictatorial. Our result implies an incompatibility between ordinal and evaluative approaches to social choice theory under 2 weak assumptions: respect for unanimity and independence of evaluation of each alternative. We describe possibilities when the latter assumption is relaxed. On the other hand, our impossibility generalises to the case where there are more than the two evaluative levels of “approved” and “disapproved”.

Suggested Citation

  • Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    • Handle: RePEc:spr:sochwe:v:57:y:2021:i:3:d:10.1007_s00355-021-01327-w
    DOI: 10.1007/s00355-021-01327-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-021-01327-w
    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/s00355-021-01327-w?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. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    2. 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, December.
    3. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    4. 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.
    5. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    6. Jean-François Laslier & M. Remzi Sanver, 2010. "Introduction to the Handbook on Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 1-12, Springer.
    7. Macé, Antonin, 2018. "Voting with evaluations: Characterizations of evaluative voting and range voting," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 10-17.
    8. Bilge Yilmaz & Murat R. Sertel, 1999. "The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 615-627.
    9. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    10. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    11. Gaertner, Wulf & Xu, Yongsheng, 2012. "A general scoring rule," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 193-196.
    12. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    13. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    14. 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.
    15. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
    16. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 409-420.
    17. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    18. Michel Balinski & Rida Laraki, 2020. "Majority judgment vs. majority rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 429-461, March.
    19. Michel Balinski & Rida Laraki, 2011. "Majority Judgment: Measuring, Ranking, and Electing," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015137, December.
    20. Donald Saari & Jill Newenhizen, 1988. "The problem of indeterminacy in approval, multiple, and truncated voting systems," Public Choice, Springer, vol. 59(2), pages 101-120, November.
    21. Claude Hillinger, 2005. "The Case for Utilitarian Voting," Homo Oeconomicus, Institute of SocioEconomics, vol. 23, pages 295-321.
    22. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    23. Steven Brams & Peter Fishburn & Samuel Merrill, 1988. "The responsiveness of approval voting: Comments on Saari and Van Newenhizen," Public Choice, Springer, vol. 59(2), pages 121-131, November.
    24. Aleskerov, Fuad & Yakuba, Vyacheslav & Yuzbashev, Dmitriy, 2007. "A `threshold aggregation' of three-graded rankings," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 106-110, January.
    25. M. Remzi Sanver, 2010. "Approval as an Intrinsic Part of Preference," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 469-481, Springer.
    26. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
    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. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    2. Guy Barokas & Yves Sprumont, 2022. "The broken Borda rule and other refinements of approval ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 187-199, January.
    3. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, 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. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    2. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    3. Antonin Macé, 2017. "Voting with evaluations: characterizations of evaluative voting and range voting," Working Papers halshs-01222200, HAL.
    4. Antonin Macé, 2015. "Voting with Evaluations: When Should We Sum? What Should We Sum?," AMSE Working Papers 1544, Aix-Marseille School of Economics, France, revised 29 Oct 2015.
    5. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    6. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    7. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    8. Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
    9. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, April.
    10. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    11. Antoinette Baujard & Frédéric Gavrel & Herrade Igersheim & Jean-François Laslier & Isabelle Lebon, 2013. "Who’s Favored by Evaluative Voting ? An Experiment Conducted During the 2012 French Presidential Election," Working Papers of BETA 2013-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    12. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon, 2020. "Some regrettable grading scale effects under different versions of evaluative voting," Working Papers halshs-02926780, HAL.
    13. Klaus Nehring & Marcus Pivato, 2022. "The median rule in judgement aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1051-1100, June.
    14. Gilbert Laffond & Jean Lainé, 2012. "Searching for a Compromise in Multiple Referendum," Group Decision and Negotiation, Springer, vol. 21(4), pages 551-569, July.
    15. Antoinette Baujard & Herrade Igersheim & Isabelle Lebon, 2021. "Some regrettable grading scale effects under different versions of evaluative voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 803-834, May.
    16. Abdelhalim El Ouafdi & Dominique Lepelley & Hatem Smaoui, 2020. "On the Condorcet efficiency of evaluative voting (and other voting rules) with trichotomous preferences," Annals of Operations Research, Springer, vol. 289(2), pages 227-241, June.
    17. Kotaro Suzumura, 2002. "Introduction to social choice and welfare," Temi di discussione (Economic working papers) 442, Bank of Italy, Economic Research and International Relations Area.
    18. Macé, Antonin, 2018. "Voting with evaluations: Characterizations of evaluative voting and range voting," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 10-17.
    19. González, Stéphane & Laruelle, Annick & Solal, Philippe, 2017. "Neutral candidates in approval and disapproval vote," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. 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.

    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:57:y:2021:i:3:d:10.1007_s00355-021-01327-w. 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.