Skip to main content
SpringerLink
Log in

The senatorial election in Spain. Proportional Borda methods for selecting several candidates

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Firstly, in this paper, we analyze how the electors vote in the Senate election in Spain. We show examples in which the election outcome is predictable and not proportional. We also show similar examples for other social choice problems, in which the strategic vote affords a great advantage to those who put it into practice.

Secondly, we introduce the definition of a proportional social choice method. We then prove the main result that determines the only Borda type social choice method that has the same proportionality as a given divisor method.

We include results with the vote thresholds that guarantee the candidates will be elected under Limited Approval Voting and, finally, compare these thresholds with the proportional Borda Method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balinski, M. L., & Young, H. P. (1982). Fair representation: Meeting the ideal of one man, one vote. New Haven: Yale University Press.

    Google Scholar 

  • Brams, S. J. (1993). Approval voting and the good society. Political Economy of the Good Society Newsletter, 3(1), 10–14.

    Google Scholar 

  • Brams, S. J., & Fishburn, P. C. (1983). Approval voting. Boston: Birkhäuser.

    Google Scholar 

  • Carbó, S., Palomares, A., & Ramírez, V. (2004). La regulación de los organos de gobierno de las cajas de ahorros: Consideraciones electorales. Hacienda Pública Española, 171, 33–55.

    Google Scholar 

  • Marín, L. (2003). Constitución Española. Aranzadi. http://www.congreso.es/funciones/constitucion/indice.htm

  • Palomares, A., & Ramírez, V. (2003). Thresholds of the divisor methods. Numerical Algorithms, 34, 405–415.

    Article  Google Scholar 

  • Ramírez, V. (2004). From principles of representation to the electoral methods. In Meeting on analysis and design of electoral systems. Oberwolfach, Germany.

  • Ramírez, V., & Palomares, A. (2002). Aspectos matemáticos en las elecciones a claustro Universitario de acuerdo con la LOU. Gaceta de la RSME, 5.3, 589–619.

    Google Scholar 

  • Ramírez, V., Pérez, R., & Márquez, M. L. (1997). Distribución de los escaños del Senado por Comunidades Autónomas. Revista de las Cortes Generales, 41.

  • Saari, D. G. (1994). Geometry of voting. New York: Springer.

    Google Scholar 

  • Saari, D. G. (2001). Chaotic elections!—A mathematician looks at voting. Providence: AMS.

    Google Scholar 

  • Spanish electoral data, Congress and Senate. http://www.elecciones.mir.es/MIR/jsp/resultados/index.htm

  • Taylor, A. D. (1995). Mathematics and politics. New York: Springer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento Matemática Aplicada, Universidad de Granada, 18071, Granada, Spain

    V. Ramírez & A. Palomares

Authors
  1. V. Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Palomares
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Ramírez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramírez, V., Palomares, A. The senatorial election in Spain. Proportional Borda methods for selecting several candidates. Ann Oper Res 158, 21–32 (2008). https://doi.org/10.1007/s10479-007-0250-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-007-0250-9

Keywords

Search

Navigation