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Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities

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  • Gallagher, Michael

Abstract

The relationship between electoral systems can be examined on a number of dimensions. Seat allocation methods are conveniently divided into two groups: those based on largest remainders and those based on highest averages. The single transferable vote has its own distinct characteristics. Focusing on certain elements – the quota, thresholds, paradoxes and the conditions under which a majority of seats can be won – enables comparisons to be drawn between seat allocation methods. Certain seat allocation methods conventionally seen as variants of proportional representation (PR) cannot be regarded as such. PR methods can be rank ordered according to whether, when complete proportionality is not attainable, they display electoral bias towards larger or smaller parties. However, a definitive ordering is elusive, since some methods that are generally more favourable to larger parties can in some circumstances set lower thresholds of representation than methods generally favourable to smaller parties.

Suggested Citation

  • Gallagher, Michael, 1992. "Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities," British Journal of Political Science, Cambridge University Press, vol. 22(4), pages 469-496, October.
  • Handle: RePEc:cup:bjposi:v:22:y:1992:i:04:p:469-496_00
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    Cited by:

    1. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
    2. Maria Rosaria Alfano & Anna Laura Baraldi & Erasmo Papagni, 2016. "Effect of the proportionality degree of electoral systems on corruption," Environment and Planning C, , vol. 34(8), pages 1895-1916, December.
    3. Siamak F. Shahandashti, 2016. "Electoral Systems Used around the World," Papers 1605.01343, arXiv.org, revised Oct 2016.
    4. 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.
    5. Alfano, Maria Rosaria & Baraldi, Anna Laura & Papagni, Erasmo, 2014. "Electoral Systems and Corruption: the Effect of the Proportionality Degree," MPRA Paper 53138, University Library of Munich, Germany, revised 11 Nov 2013.
    6. Grofman, Bernard & Feld, Scott L. & Fraenkel, Jon, 2017. "Finding the Threshold of Exclusion for all single seat and multi-seat scoring rules: Illustrated by results for the Borda and Dowdall rules," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 52-56.
    7. Pellicer, Miquel & Wegner, Eva, 2013. "Electoral Rules and Clientelistic Parties: A Regression Discontinuity Approach," Quarterly Journal of Political Science, now publishers, vol. 8(4), pages 339-371, October.
    8. Jessica Fortin-Rittberger & Berthold Rittberger, 2014. "Do electoral rules matter? Explaining national differences in women's representation in the European Parliament," European Union Politics, , vol. 15(4), pages 496-520, December.
    9. Jones, Michael A. & Wilson, Jennifer M., 2010. "Evaluation of thresholds for power mean-based and other divisor methods of apportionment," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 343-348, May.
    10. Sorokin, Constantine & Zakharov, Alexei, 2018. "Vote-motivated candidates," Journal of Economic Theory, Elsevier, vol. 176(C), pages 232-254.
    11. Gwizdalla, Tomasz M., 2008. "Gallagher index for sociophysical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2937-2951.
    12. M. Rosaria Alfano & A. Laura Baraldi, 2014. "Electoral Systems and Economic Growth: What is the Importance of the Proportionality Degree?," EERI Research Paper Series EERI RP 2014/06, Economics and Econometrics Research Institute (EERI), Brussels.
    13. José Gutiérrez, 2015. "Majorization comparison of closed list electoral systems through a matrix theorem," Annals of Operations Research, Springer, vol. 235(1), pages 807-814, December.
    14. Alexei Zakharov, 2012. "Probabilistic voting equilibria under nonlinear candidate payoffs," Journal of Theoretical Politics, , vol. 24(2), pages 235-247, April.
    15. Kangas, Annika & Laukkanen, Sanna & Kangas, Jyrki, 2006. "Social choice theory and its applications in sustainable forest management--a review," Forest Policy and Economics, Elsevier, vol. 9(1), pages 77-92, November.
    16. Alexei Zakharov & Constantine Sorokin, 2014. "Policy convergence in a two-candidate probabilistic voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 429-446, August.

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