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Apportionment in times of digitalization

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  • Tanguiane, Andranick S.

Abstract

We critically discuss the Jefferson/D'Hondt and Webster/Sainte-Laguë methods, which are used to allocate parliament seats to parties in the mixed-member proportional representation systems in Germany, New Zealand, Bolivia, South Africa, South Korea, Scotland and Wales, as well as in the European Parliament. The task is as follows: (1) the parliament must be of a certain size or slightly larger than that, (2) the party factions must include all direct mandate holders elected in constituencies and (3) the faction ratio should reflect, with a certain accuracy, the votes received by the parties across the country. We show that discrete optimization techniques result in better and more accurate apportionments. In addition, we consider adjustment vote weights defined within the optimization approach and show that they can give a general consistent solution to the apportionment problem. All of these are illustrated using the example of the 2021 German Bundestag elections.

Suggested Citation

  • Tanguiane, Andranick S., 2023. "Apportionment in times of digitalization," Working Paper Series in Economics 161, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    • Handle: RePEc:zbw:kitwps:161
    DOI: 10.5445/IR/1000170725
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    References listed on IDEAS

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    1. Diego Varela & Javier Prado-Dominguez, 2012. "Negotiating the Lisbon Treaty: Redistribution, Efficiency and Power Indices," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 6(2), pages 107-124, July.
    2. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    3. M. L. Balinski & H. P. Young, 1979. "Criteria for Proportional Representation," Operations Research, INFORMS, vol. 27(1), pages 80-95, February.
    4. Carmen Herrero & Ricardo Martínez, 2008. "Balanced allocation methods for claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 603-617, May.
    5. Brendan O'Leary & Bernard Grofman & Jørgen Elklit, 2005. "Divisor Methods for Sequential Portfolio Allocation in Multi‐Party Executive Bodies: Evidence from Northern Ireland and Denmark," American Journal of Political Science, John Wiley & Sons, vol. 49(1), pages 198-211, January.
    6. Mariusz Mazurkiewicz & Jacek W. Mercik, 2005. "Modified Shapley-Shubik power index for parliamentary coalitions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 15(2), pages 43-52.
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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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