New indexes for measuring electoral disproportionality

  1. VERÓNICA ARREDONDO 1
  2. MIGUEL MARTÍNEZ-PANERO 2
  3. ANTONIO PALOMARES 3
  4. TERESA PEÑA 2
  5. VICTORIANO RAMÍREZ 3
  1. 1 Universidad Autónoma de Zacatecas
    info

    Universidad Autónoma de Zacatecas

    Zacatecas, México

    ROR https://ror.org/01m296r74

  2. 2 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

  3. 3 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

Revista:
Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

ISSN: 1575-605X

Ano de publicación: 2020

Volume: 21

Número: 2

Páxinas: 161-178

Tipo: Artigo

DOI: 10.24309/RECTA.2020.21.2.05 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Outras publicacións en: Rect@: Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

Obxectivos de Desenvolvemento Sustentable

Resumo

The number of representatives obtained by each political party in an electoral process must be a whole number. So, the percentage of votes for each party usually differs from the corresponding percentage of seats, forcing a certain unavoidable disproportionality. On the other hand, different elements of the electoral system (constituencies, thresholds, etc.) may produce some avoidable disproportionality. Those indexes traditionally used to analyse disproportionality take into account an unreachable exact proportionality as a reference. Instead, our more realistic approach quantifies distortions from a specific allotment, namely the seat distribution obtained when applying a proportional method to the total votes (that is, as if it were a unique constituency, without electoral thresholds or incentives to the winning party). Hence, we measure the avoidable disproportionality associated with such method. Unlike traditional indexes, we propose indexes associated with proportional allotment methods that can be zero in real situations. They are simple to calculate and allow us to decipher the number of seats assigned beyond the inevitable disproportionality which arises from the constraint of whole numbers. We are particularly interested in the indexes associated with Jefferson and Webster methods, which are compared to Gallagher, Loosemore-Hanby and SainteLaguë indexes for the results of 55 elections held in several countries.

Referencias bibliográficas

  • M.L. Balinski and H.P. Young, Brookings Institution Press, Fair Representation: Meeting the Ideal of One Man, One Vote (Washington, D.C., 2001)
  • F, Pukelsheim, Proportional Representation. Apportionment Methods and Their Applications, Cham: Springer International Publishing (2014).
  • M. Gallagher, Proportionality, disproportionality and electoral systems. Electoral Studies 10 (1991) 33–51.
  • M. Suojanen, Proportionality in the European Parliamentary Elections: Evidence since 1979. Representation 42 (2006) 103–116.
  • A. Karpov, Measurement of Disproportionality in Proportional Representations Systems. Mathematical and Computer Modelling 48 (2008) 1421–1438.
  • R. Taagepera and B. Grofman, Mapping the indexes of seats-votes disproportionality and interelection volatility, Party Politics 9 (6) (2003) 659–677.
  • R. Taagepera, Predicting Party Sizes. The Logic of Simple Electoral Systems, Oxford: Oxford University Press (2007).
  • M. Koppel and A. Diskin, Measuring disproportionality, volatility and malapportionment: Axiomatization and solutions, Social Choice and Welfare 33 (2009) 281–286.
  • D. Boyssou, T. Marchant and M. Pirlot, A characterization of two disproportionality and malapportionment indices: the Duncan and Duncan index and the Lijphart index, Annals of Operations Research (2019). DOI: 10.1007/s10479-018-3073-y
  • A. Palomares, F. Pukelsheim and V. Ramírez, The whole and its parts: On the coherence theorem of Balinski and Young, Mathematical Social Sciences 83 (2016) 11–19.
  • H.F Niemeyer and A.C. Niemeyer, Alice C, Apportionment Methods” in Mathematical Social Sicences 56 (2008) 240-253.
  • A. Palomares and V. Ramírez, Thresholds of the divisor methods. Numerical Algorithms 34 (2003) 405–415.
  • A. Karpov, Alliance incentives under the D’Hondt method, Mathematical Social Sciences 74 (2015) 1–7.
  • D. Nohlen, Gramática de los Sistemas Electorales [Grammar of Electoral Systems], Madrid: Tecnos (2015).
  • J. Loosemore and V.J. Hanby, The theoretical limits of maximum distortion: Some analytic expressions of electoral systems, British Journal of Political Science 1 (1971) 467–477.
  • M. Laakso and R. Taagapera, Effective Number of Parties: A measure with application to West Europe, Comparative Political Studies, 12(1) (1979), 3-27.
  • B.L. Monroe, Disproportionality and Malapportionment: Measuring Electoral Inequity, Electoral Studies 13 (1994) 132–49.
  • J. Goldenberg and S.D. Fisher, The Sainte-Laguë index of disproportionality and Dalton’s principle of transfers, Party Politics 25(2) (2017) 203–207.
  • G. Borisyuk, C. Rallings, and M. Thrasher, Selecting indexes of electoral proportionality: General properties and relationships, Quality and Quantity 38 (2004) 51–74.
  • M. L. Balinski and V. Ramírez, Parametric methods of apportionment, rounding and production, Mathematical Social Sciences 37(2) (1999) 107–122.
  • M. Martínez-Panero, V. Arredondo, T. Peña and V. Ramírez, A new quota approach to electoral disproportionality. Economies 7(1) 17 (2019); doi:10.3390/economies7010017.
  • C. Bedock and N.Sauger, Electoral systems with a majority bonus as unconventional mixed systems, Representation 50 (1) (2014) 99–112.
  • M.L. Balinski and F. Pukelsheim, Matrices and politics. In Tampere Liski, E.P., Isotalo, J., Niemelä, J., Puntanen, S., & Styan, G.P.H. (Eds.), Festschrift for Tarmo Pukkila on his 60th Birthday, University of Tampere (Finland, 2006), pp. 233–242.
  • V. Ramírez, B.L. Delgado and A. López, Electoral System in Poland: Revision and Proposal of Modification Based on Biproportionality, Representation 51 (2015) 187-204.