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Reformulating the Cube Law for Proportional Representation Elections

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  • Taagepera, Rein

Abstract

The cube law was proposed around 1910 to express the conversion of a party's vote shares into its seat share in two-party plurality elections with single-seat districts. This article develops predictive seat-vote equations for a much wider range of elections, including those involving many parties, single- and multi-seat districts, and diverse seat allocation rules such as plurality and list proportional representation (PR). Without any statistical curve fitting based on the seat and vote shares themselves, the basic features of the conversion are predicted using exogenous parameters: magnitude and number of districts, number of parties, and total size of the electorate and of the assembly. The link between the proposed equations and the original cube law is explicated. Using an existing data base, the fit of the predictive model is examined. On balance, this model accounts well for the conversion of votes to seats, and for the deviation from proportionality in PR systems.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:apsrev:v:80:y:1986:i:02:p:489-504_18
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    Cited by:

    1. Konstantinos Matakos & Orestis Troumpounis & Dimitrios Xefteris, 2015. "Turnout and Polarization Under Alternative Electoral Systems," Studies in Political Economy, in: Norman Schofield & Gonzalo Caballero (ed.), The Political Economy of Governance, edition 127, pages 335-362, Springer.
    2. Kåre Vernby, 2007. "Strikes are more common in countries with majoritarian electoral systems," Public Choice, Springer, vol. 132(1), pages 65-84, July.
    3. Dario Debowicz & Alejandro Saporiti & Yizhi Wang, 2021. "Redistribution, power sharing and inequality concern," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 197-228, August.
    4. Pinheiro, Flavio, 2014. "A Protectionist Bias in Proportional Politics: Assessing How Electoral Institutions Affect Tariff Levels," SocArXiv xp5zm, Center for Open Science.
    5. Kaare Strom, 1989. "Inter-party Competition in Advanced Democracies," Journal of Theoretical Politics, , vol. 1(3), pages 277-300, July.
    6. 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).
    7. Andersen, Jørgen Juel & Heggedal, Tom-Reiel, 2019. "Political rents and voter information in search equilibrium," Games and Economic Behavior, Elsevier, vol. 114(C), pages 146-168.
    8. Rein Taagepera, 2001. "Party Size Baselines Imposed by Institutional Constraints," Journal of Theoretical Politics, , vol. 13(4), pages 331-354, October.
    9. 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.
    10. Geoffrey Pritchard & Mark C. Wilson, 2023. "Multi-district preference modelling," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(1), pages 587-613, February.
    11. Bol, Damien & Matakos, Konstantinos & Troumpounis, Orestis & Xefteris, Dimitrios, 2019. "Electoral rules, strategic entry and polarization," Journal of Public Economics, Elsevier, vol. 178(C).

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