IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v54y2020i1d10.1007_s00355-019-01208-3.html
   My bibliography  Save this article

The expanding approvals rule: improving proportional representation and monotonicity

Author

Listed:
  • Haris Aziz

    (UNSW Sydney and Data61 CSIRO)

  • Barton E. Lee

    (UNSW Sydney and Data61 CSIRO)

Abstract

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to look towards the single transferable vote (STV) rule as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called the expanding approvals rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.

Suggested Citation

  • Haris Aziz & Barton E. Lee, 2020. "The expanding approvals rule: improving proportional representation and monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 1-45, January.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:1:d:10.1007_s00355-019-01208-3
    DOI: 10.1007/s00355-019-01208-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-019-01208-3
    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/s00355-019-01208-3?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. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    2. Ariel Procaccia & Jeffrey Rosenschein & Aviv Zohar, 2008. "On the complexity of achieving proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 353-362, April.
    3. 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.
    4. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    5. D. Marc Kilgour, 2010. "Approval Balloting for Multi-winner Elections," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 105-124, Springer.
    6. 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.
    7. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    8. Geller, Chris, 2002. "Single transferable vote with borda elimination: a new vote counting system," Working Papers eco_2002_01, Deakin University, Department of Economics.
    9. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
    10. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    11. Debord, Bernard, 1993. "Prudent k-choice functions: properties and algorithms," Mathematical Social Sciences, Elsevier, vol. 26(1), pages 63-77, July.
    12. Nicolaus Tideman & Daniel Richardson, 2000. "Better Voting Methods Through Technology: The Refinement-Manageability Trade-Off in the Single Transferable Vote," Public Choice, Springer, vol. 103(1), pages 13-34, April.
    13. Fuad Aleskerov & Alexander Karpov, 2013. "A new single transferable vote method and its axiomatic justification," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 771-786, March.
    14. Nicolaus Tideman, 1995. "The Single Transferable Vote," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 27-38, Winter.
    15. Salvador Barberà & Danilo Coelho, 2008. "How to choose a non-controversial list with k names," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 79-96, June.
    16. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    17. M. Sanver & William Zwicker, 2009. "One-way monotonicity as a form of strategy-proofness," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 553-574, November.
    18. Gehrlein, William V., 1985. "The Condorcet criterion and committee selection," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 199-209, December.
    19. Tideman, Nicolaus & Richardson, Daniel, 2000. "Better Voting Methods through Technology: The Refinement-Manageabililty Trade-Off in the Single Transferable Vote," Public Choice, Springer, vol. 103(1-2), pages 13-34, April.
    20. 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. Dominik Peters & Grzegorz Pierczy'nski & Piotr Skowron, 2020. "Proportional Participatory Budgeting with Additive Utilities," Papers 2008.13276, arXiv.org, revised Oct 2022.
    2. Aziz, Haris & Lee, Barton E., 2022. "A characterization of proportionally representative committees," Games and Economic Behavior, Elsevier, vol. 133(C), pages 248-255.
    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Kamesh Munagala & Zeyu Shen & Kangning Wang, 2021. "Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule," Papers 2106.00091, arXiv.org.

    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. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    2. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
    3. Piotr Faliszewski & Piotr Skowron & Arkadii Slinko & Nimrod Talmon, 2018. "Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 513-550, October.
    4. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    5. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency," Working Papers halshs-01817943, HAL.
    6. Egor Ianovski, 2022. "Electing a committee with dominance constraints," Annals of Operations Research, Springer, vol. 318(2), pages 985-1000, November.
    7. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    8. Martin Lackner & Piotr Skowron, 2017. "Consistent Approval-Based Multi-Winner Rules," Papers 1704.02453, arXiv.org, revised Oct 2019.
    9. Aziz, Haris & Lee, Barton E., 2022. "A characterization of proportionally representative committees," Games and Economic Behavior, Elsevier, vol. 133(C), pages 248-255.
    10. Eric Kamwa, 2022. "The Condorcet Loser Criterion in Committee Selection," Working Papers hal-03880064, HAL.
    11. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    12. Diss, Mostapha & Mahajne, Muhammad, 2020. "Social acceptability of Condorcet committees," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 14-27.
    13. 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.
    14. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    15. Maksim Gladyshev, 2019. "Vulnerability Of Voting Paradoxes As A Criteria For Voting Procedure Selection," HSE Working papers WP BRP 70/PS/2019, National Research University Higher School of Economics.
    16. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    17. Gilbert Laffond & Jean Lainé, 2012. "Searching for a Compromise in Multiple Referendum," Group Decision and Negotiation, Springer, vol. 21(4), pages 551-569, July.
    18. Mostapha Diss & Ahmed Doghmi, 2016. "Multi-winner scoring election methods: Condorcet consistency and paradoxes," Public Choice, Springer, vol. 169(1), pages 97-116, October.
    19. 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.
    20. Kamesh Munagala & Yiheng Shen & Kangning Wang & Zhiyi Wang, 2021. "Approximate Core for Committee Selection via Multilinear Extension and Market Clearing," Papers 2110.12499, arXiv.org.

    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:54:y:2020:i:1:d:10.1007_s00355-019-01208-3. 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.