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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
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    2. 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.

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    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

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