IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v182y2020i1d10.1007_s11127-019-00680-w.html
   My bibliography  Save this article

Pot and ladle: a formula for estimating the distribution of seats under the Jefferson–D’Hondt method

Author

Listed:
  • Jarosław Flis

    (Jagiellonian University)

  • Wojciech Słomczyński

    (Jagiellonian University)

  • Dariusz Stolicki

    (Jagiellonian University)

Abstract

We propose a simple yet new formula for estimating national seat shares and quantifying seat biases in elections employing the Jefferson–D’Hondt (JDH) method for seat allocation. It is based solely on the national vote shares and fixed parameters of the given electoral system. The proposed formula clarifies the relationship between seat bias on the one hand, and the number of parties and the number of districts on the other. We demonstrate that the formula provides a good estimate of seat allocations in real-life elections even in the case of minor violations of the underlying assumptions. With that aim in mind, we have tested it for all nine EU countries that employ the JDH method in parliamentary elections. Moreover, we discuss the applications of the formula for modeling the effects of vote swings, coalition formation and breakup, spoiler effects, electoral engineering, artificial thresholds and political gerrymandering. By not requiring district-level vote shares, our formula simplifies electoral simulations using the JDH method.

Suggested Citation

  • Jarosław Flis & Wojciech Słomczyński & Dariusz Stolicki, 2020. "Pot and ladle: a formula for estimating the distribution of seats under the Jefferson–D’Hondt method," Public Choice, Springer, vol. 182(1), pages 201-227, January.
    • Handle: RePEc:kap:pubcho:v:182:y:2020:i:1:d:10.1007_s11127-019-00680-w
    DOI: 10.1007/s11127-019-00680-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11127-019-00680-w
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11127-019-00680-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 search for a different version of it.

    References listed on IDEAS

    as
    1. Marek M. Kaminski, 2002. "Do Parties Benefit from Electoral Manipulation? Electoral Laws and Heresthetics in Poland, 1989-93," Journal of Theoretical Politics, , vol. 14(3), pages 325-358, July.
    2. Svante Janson, 2014. "Asymptotic bias of some election methods," Annals of Operations Research, Springer, vol. 215(1), pages 89-136, April.
    3. Linzer, Drew A., 2012. "The Relationship between Seats and Votes in Multiparty Systems," Political Analysis, Cambridge University Press, vol. 20(3), pages 400-416, July.
    4. Frederic Udina & Pedro Delicado, 2005. "Estimating Parliamentary composition through electoral polls," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 387-399, March.
    5. Katz, Jonathan N. & King, Gary, 1999. "A Statistical Model for Multiparty Electoral Data," American Political Science Review, Cambridge University Press, vol. 93(1), pages 15-32, March.
    6. Taagepera, Rein, 1986. "Reformulating the Cube Law for Proportional Representation Elections," American Political Science Review, Cambridge University Press, vol. 80(2), pages 489-504, June.
    7. Lijphart, Arend, 1990. "The Political Consequences of Electoral Laws, 1945–85," American Political Science Review, Cambridge University Press, vol. 84(2), pages 481-496, June.
    8. Ernesto Calvo & Jonathan Rodden, 2015. "The Achilles Heel of Plurality Systems: Geography and Representation in Multiparty Democracies," American Journal of Political Science, John Wiley & Sons, vol. 59(4), pages 789-805, October.
    9. Huntington, Edward V., 1931. "Methods of Apportionment in Congress," American Political Science Review, Cambridge University Press, vol. 25(4), pages 961-965, November.
    10. Marek M. Kaminski, 2018. "Spoiler effects in proportional representation systems: evidence from eight Polish parliamentary elections, 1991–2015," Public Choice, Springer, vol. 176(3), pages 441-460, September.
    11. Balinski, M. L. & Young, H. P., 1978. "Stability, Coalitions and Schisms in Proportional Representation Systems," American Political Science Review, Cambridge University Press, vol. 72(3), pages 848-858, September.
    12. Karpov, Alexander, 2015. "Alliance incentives under the D’Hondt method," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 1-7.
    13. Benoit, Kenneth, 2000. "Which Electoral Formula Is the Most Proportional? A New Look with New Evidence," Political Analysis, Cambridge University Press, vol. 8(4), pages 381-388, July.
    14. Mathias Drton & Udo Schwingenschlögl, 2005. "Asymptotic seat bias formulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 23-31, September.
    15. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
    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. Sanjay Bhattacherjee & Palash Sarkar, 2023. "On Using Proportional Representation Methods as Alternatives to Pro-Rata Based Order Matching Algorithms in Stock Exchanges," Papers 2303.09652, arXiv.org, revised Nov 2023.
    2. Andreas Darmann & Christian Klamler, 2023. "Does the rule matter? A comparison of preference elicitation methods and voting rules based on data from an Austrian regional parliamentary election in 2019," Public Choice, Springer, vol. 197(1), pages 63-87, October.

    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. Karpov, Alexander, 2015. "Alliance incentives under the D’Hondt method," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 1-7.
    2. Bittó, Virág, 2017. "Az Imperiali és Macau politikai választókörzet-kiosztási módszerek empirikus vizsgálata [Empirical Analysis of the Imperiali and Macau Apportionment Methods]," MPRA Paper 79554, University Library of Munich, Germany.
    3. Heinrich Lothar & Pukelsheim Friedrich & Schwingenschlögl Udo, 2005. "On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence," Statistics & Risk Modeling, De Gruyter, vol. 23(2/2005), pages 117-129, February.
    4. Balázs R Sziklai & Károly Héberger, 2020. "Apportionment and districting by Sum of Ranking Differences," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    5. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    6. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.
    7. De Santo, Alessia & Le Maux, Benoît, 2023. "On the optimal size of legislatures: An illustrated literature review," European Journal of Political Economy, Elsevier, vol. 77(C).
    8. Frederic Udina & Pedro Delicado, 2005. "Estimating Parliamentary composition through electoral polls," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 387-399, March.
    9. Arzheimer, Kai & Evans, Jocelyn, 2010. "Bread and butter à la française: Multiparty forecasts of the French legislative vote (1981-2007)," International Journal of Forecasting, Elsevier, vol. 26(1), pages 19-31, January.
    10. Alessandro Gavazza & Mattia Nardotto & Tommaso Valletti, 2019. "Internet and Politics: Evidence from U.K. Local Elections and Local Government Policies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 2092-2135.
    11. Julia Cage & Edgard Dewitte, 2021. "It Takes Money to Make MPs: Evidence from 150 Years of British Campaign Spending," Sciences Po publications 2021-08, Sciences Po.
    12. Udo Schwingenschlögl, 2008. "Asymptotic Equivalence of Seat Bias Models," Statistical Papers, Springer, vol. 49(2), pages 191-200, April.
    13. T. H. A. Nguyen & T. Laurent & C. Thomas-Agnan & A. Ruiz-Gazen, 2022. "Analyzing the impacts of socio-economic factors on French departmental elections with CoDa methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(5), pages 1235-1251, April.
    14. Yifeng Liu & Yuan Lai, 2024. "Analyzing jogging activity patterns and adaptation to public health regulation," Environment and Planning B, , vol. 51(3), pages 670-688, March.
    15. Baskaran, Thushyanthan & Lopes da Fonseca, Mariana, 2013. "Electoral thresholds and political outcomes: Quasi-experimental evidence from a reform in Germany," University of Göttingen Working Papers in Economics 177, University of Goettingen, Department of Economics.
    16. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," CERS-IE WORKING PAPERS 1716, Institute of Economics, Centre for Economic and Regional Studies.
    17. Steven J. Brams & Markus Brill & Anne-Marie George, 2022. "The excess method: a multiwinner approval voting procedure to allocate wasted votes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 283-300, February.
    18. Bekkouche, Yasmine & Cagé, Julia & Dewitte, Edgard, 2022. "The heterogeneous price of a vote: Evidence from multiparty systems, 1993–2017," Journal of Public Economics, Elsevier, vol. 206(C).
    19. Grimmett, G.R. & Oelbermann, K.-F. & Pukelsheim, F., 2012. "A power-weighted variant of the EU27 Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 136-140.
    20. Schwingenschlögl, Udo & Drton, Mathias, 2006. "Seat excess variances of apportionment methods for proportional representation," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1723-1730, October.

    More about this item

    Keywords

    Jefferson–D’Hondt method; Seats-votes relationship; Seat bias; Proportional representation;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

    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:kap:pubcho:v:182:y:2020:i:1:d:10.1007_s11127-019-00680-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.