IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2023_006.html
   My bibliography  Save this paper

MMP-Elections: Equal Influence and Controlled Assembly Size

Author

Listed:
  • Stensholt, Eivind

    (Dept. of Business and Management Science, Norwegian School of Economics)

Abstract

In an MMP election (Mixed Member Proportional) of a legislature, a QP-ballot supports party Q in a single-seat constituency and a list of candidates from P. With ꙍ(j) constituency seats won and list support in z(Pj) ballots, party Pj wins α(j) list seats, so that ꙍ(j)+α(j) becomes proportional to z(Pj). The pivotal party, Pj*, has the highest of all ratios ꙍ(j)/z(Pj). Proportionality implies, for all Pj passing some threshold, that [ꙍ(j)+α(j)]/z(Pj) ≥ ꙍ(j*)/z(Pj*). In the smallest proportional assembly, all ≥ are equalities and α(j*)=0. The pivotal party’s list support, z(Pj*), is naturally volatile. An election with α(j*)=0 tells that z(Pj*) list votes were wasted, and many voters learn it. Thus, between Bundestag elections 2017 and 2021, z(Pj*) dropped significantly. The smallest possible size of a proportional assembly rose from 709 to 794 seats, while the legal norm is 598. But an ad-hoc law of 2020 abandoned the proportionality rule, shrinking the assembly from 794 to 736 seats. ꙍ(j) measures and records the success of party Pj in the single-seat tallies; it also records how much α(j) is reduced by Pj’s constituency success. The paper compares this”traditional accounting” and“faithful accounting”: The latter records a QiPj-ballot, with Qi as constituency winner, with a tiny seat fraction that reduces α(j). Traditional accounting treats party Pj as a basic entity. Faithful accounting replaces it by the set Λ(Pj) of voters with list vote for Pj. This is a paradigm shift: Traditional accounting works even if constituency votes and list votes are collected in separate ballot boxes. But in faithful accounting, each ballot’s combination of Qi and Pj is essential. Main results: The change from traditional to faithful accounting brings the assembly size under control. A large inequality in voters influence is substantially reduced.

Suggested Citation

  • Stensholt, Eivind, 2023. "MMP-Elections: Equal Influence and Controlled Assembly Size," Discussion Papers 2023/6, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2023_006
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/11250/3070065
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dowding, Keith & Van Hees, Martin, 2008. "In Praise of Manipulation," British Journal of Political Science, Cambridge University Press, vol. 38(1), pages 1-15, January.
    Full references (including those not matched with items on IDEAS)

    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. Brian Kogelmann, 2017. "Aggregating out of indeterminacy," Politics, Philosophy & Economics, , vol. 16(2), pages 210-232, May.
    2. Stensholt, Eivind, 2020. "Anomalies of Instant Runoff Voting," Discussion Papers 2020/6, Norwegian School of Economics, Department of Business and Management Science.
    3. Hugh Ward & Albert Weale, 2010. "Is Rule by Majorities Special?," Political Studies, Political Studies Association, vol. 58(1), pages 26-46, February.
    4. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    5. Wesley H. Holliday & Eric Pacuit, 2021. "Measuring Violations of Positive Involvement in Voting," Papers 2106.11502, arXiv.org.
    6. Nicholas R. Miller, 2019. "Reflections on Arrow’s theorem and voting rules," Public Choice, Springer, vol. 179(1), pages 113-124, April.
    7. Ulle Endriss, 2013. "Sincerity and manipulation under approval voting," Theory and Decision, Springer, vol. 74(3), pages 335-355, March.
    8. Stensholt, Eivind, 2015. "What Happened in Burlington?," Discussion Papers 2015/26, Norwegian School of Economics, Department of Business and Management Science.
    9. Edgardo Bucciarelli & Andrea Oliva, 2020. "Arrow’s impossibility theorem as a special case of Nash equilibrium: a cognitive approach to the theory of collective decision-making," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 19(1), pages 15-41, June.
    10. Stensholt, Eivind, 2021. "Faithful accounting in MMP-elections," Discussion Papers 2021/7, Norwegian School of Economics, Department of Business and Management Science.
    11. Bobrowski, Jakub & Łaska, Grażyna, 2023. "Using spatial elimination and ranking methods in the renewable energy investment parcel search process," Energy, Elsevier, vol. 285(C).
    12. Nuñez, M. & Valletta, G., 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    Keywords

    Mixed member proportional; equal influence; assembly size; split ballots; faithful accounting;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:nhhfms:2023_006. 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: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    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.