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A Comparison of Electoral Formulae for the Faroese Parliament

  • Petur Zachariassen
  • Martin Zachariassen
Part of the Studies in Choice and Welfare book series (WELFARE)

Abstract

The Faroese electoral system uses a method of proportional representation for distributing the seats in the Faroese Parliament (The Løgting). The electoral formulae attempt to give each political party a number of seats that is close to its vote share. In addition, each district should receive a number of delegates that is proportional to the number of voters in the district. We show that the current electoral formula has significant weaknesses, and propose 7 alternative electoral formulae which consider various subsets of constraints — such as lower bounds on the number of seats in districts and electoral thresholds. Numerical simulations with the current and proposed electoral formulae on the elections from 1978 to 2004, and on randomly generated election results, are presented. The results show that some of the proposed alternatives clearly are superior to the current electoral formula with respect to well-known quality measures.

Keywords

Electoral formula apportionment method proportional representation multimember districts biproportional rounding numerical simulations 

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References

  1. Balinski, M. L., 2002. Wahlen in Mexico — Verhältniswahlrecht häappchenweise, Spektrum der Wissenschaft, Oktober, 72–74.Google Scholar
  2. Balinski, M. L., and Demange, G., 1989a. An axiomatic approach to proportionality between matrices. Mathematics of Operations Research 14, 700–719.MathSciNetGoogle Scholar
  3. Balinski, M. L., and Demange, G., 1989b. Algorithms for proportional matrices in reals and integers. Mathematical Programming 45, 193–210.CrossRefMathSciNetGoogle Scholar
  4. Balinski, M. L., and Rachev, S. T., 1997 Rounding proportions: Methods of rounding. Mathematical Scientist 22, 1–26.MathSciNetGoogle Scholar
  5. Balinski, M. L., and Young, H. P., 2001. Fair representation: Meeting the ideal of one man, one vote. Brookings Institution Press, 2nd edition.Google Scholar
  6. Cox, L. H., and Ernst, L. R., 1982. Controlled rounding. INFOR 20(4), 423–432.Google Scholar
  7. Gallagher, M., 1991. Proportionality, disproportionality, and electoral systems. Electoral Studies 10, 33–51.CrossRefGoogle Scholar
  8. Hylland, A., 1990. Lagtinget pa Færøerne: Beskrivelse av og kommentarer til valgordningen. Handelshøyskolen BI.Google Scholar
  9. Loosemore, J., and Hanby, V. J., 1971. The theoretical limits of maximal distortion: some analytic expressions for electoral systems. British Journal of Political Science 1:4, 467–477.CrossRefGoogle Scholar
  10. Maier, S., 2006. Algorithms for Biproportional Apportionment Methods. In Mathematics and Democracy. Recent Advances in Voting Systems and Collective Choice, In Press, New York.Google Scholar
  11. Pukelsheim, F., 2000. Mandatszuteilungen bei Verhäaltniswahlen: Erfolgswertgleichheit der Wählerstimmen. Allgemeines Statistiches Archiv 84, 447–459.CrossRefMathSciNetGoogle Scholar
  12. Pukelsheim F., and Schuhmacher, C., 2004. Das neue Zürcher Zuteilungsverfahren für Parlamentswahlen. Aktuelle Juristische Praxis — Practique Juridique Actuelle 5/2004, 505–522.Google Scholar
  13. Schuster, K., Pukelsheim, F., Drton, M., and Draper, N. R., 2003. Seat biases of apportionment methods for proportional representation. Electoral Studies 22, 651–671.CrossRefGoogle Scholar
  14. Zachariasen, M., 2006. Algorithmic Aspects of Divisor-Based Biproportional Rounding. Technical Report 06-05, Department of Computer Science, University of Copenhagen.Google Scholar
  15. Zachariassen, P., 2005. Uppgerð av løgtingsvali — eitt sindur um bygnað og virknað [in Faroese]. Ársfrágreiðing 2004, Fróðskaparsetur Føroya.Google Scholar
  16. Zachariassen, P., and Zachariassen, M., 2005. A comparison of electoral formulae for the Faroese Parliament (The Løgting) [in Faroese]. Technical report NVD-rit 2005:1, NáttúruvÍsindadeildin, Fróðskaparsetur Føroya.Google Scholar

Copyright information

© Springer Berlin · Heidelberg 2006

Authors and Affiliations

  • Petur Zachariassen
    • 1
  • Martin Zachariassen
    • 2
  1. 1.University of the Faroe IslandsDenmark
  2. 2.Department of Computer ScienceUniversity of CopenhagenCopenhagen

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