ACE Project (2019). Electoral system (Chamber 1). ACE Electoral Knowledge Network. http://aceproject.org/epic-en/CDMap?question=ES005&f=. Accessed 14 May 2019.
Baldini, G., & Pappalardo, A. (2009). Elections, electoral systems and volatile voters. Basingstoke: Palgrave Macmillan.
Book
Google Scholar
Balinski, M. L., & Young, H. P. (1978a). The Jefferson method of apportionment. SIAM Review,20(3), 278–284. https://doi.org/10.1137/1020040.
Article
Google Scholar
Balinski, M. L., & Young, H. P. (1978b). Stability, coalitions and schisms in proportional representation systems. American Political Science Review,72(3), 848–858. https://doi.org/10.2307/1955106.
Article
Google Scholar
Balinski, M. L., & Young, H. P. (2001). Fair representation: Meeting the ideal of one man, one vote. Washington, DC: Brookings Institution Press.
Google Scholar
Barceló, J., & Muraoka, T. (2018). The effect of variance in district magnitude on party system inflation. Electoral Studies,54, 44–55. https://doi.org/10.1016/j.electstud.2018.04.016.
Article
Google Scholar
Benoit, K. (2000). Which electoral formula is the most proportional? A new look with new evidence. Political Analysis,8(4), 381–388. https://doi.org/10.1093/oxfordjournals.pan.a029822.
Article
Google Scholar
Blau, A. (2001). Partisan bias in British general elections. British Elections & Parties Review,11(1), 46–65. https://doi.org/10.1080/13689880108413053.
Article
Google Scholar
Bochsler, D. (2010). Who gains from apparentments under D’Hondt? Electoral Studies,29(4), 617–627. https://doi.org/10.1016/j.electstud.2010.06.001.
Article
Google Scholar
Bormann, N. C., & Golder, M. (2013). Democratic electoral systems around the world, 1946–2011. Electoral Studies,32(2), 360–369. https://doi.org/10.1016/j.electstud.2013.01.005.
Article
Google Scholar
Brancati, D. (2007). Global Elections Database. Available at: http://www.globalelectionsdatabase.com/. Accessed 12 June 2016.
Calvo, E., & Rodden, J. (2015). The Achilles heel of plurality systems: Geography and representation in multiparty democracies. American Journal of Political Science,59(4), 789–805. https://doi.org/10.1111/ajps.12167.
Article
Google Scholar
Carey J. M. (2017). Electoral system design in new democracies. In Herron, E., Pekkanen, R., & Shugart, M. S. (Eds.) Oxford handbook of electoral systems (pp. 85–111). New York: Oxford. https://doi.org/10.1093/oxfordhb/9780190258658.001.0001.
Google Scholar
Carstairs, A. M. (1980). A short history of electoral systems in Western Europe. London: George Allen & Unwin.
Google Scholar
Chafee, Z. (1929). Congressional reapportionment. Harvard Law Review,42(8), 1015–1047. https://doi.org/10.2307/1331072.
Article
Google Scholar
Colomer, J. M. (2004). The handbook of electoral system choice. London: Palgrave Macmillan.
Book
Google Scholar
D’Hondt, V. (1882). Système pratique et raisonné de représentation proportionnelle. Bruxelles: Libraire C. Muquardt. https://doi.org/10.3931/e-rara-39876.
Book
Google Scholar
D’Hondt, V. (1883). Formule du minimum dans la représentation proportionnelle. Moyen facile de trouver le diviseur. Représentation proportionnelle. Revue mensuelle 2, pp. 117–128, 129–130.
D’Hondt, V. (1885). Exposé du système pratique de représentation proportionnelle. Adopté par le Comité de l’Association Réformiste Belge. Gand: Eug. Vanderhaeghen.
Google Scholar
Dančišin, V. (2013). Hľadanie volebného deliteľa Victorom D’Hondtom. European Electoral Studies,10(1), 63–70.
Google Scholar
Deza, M. M., & Deza, E. (2014). Encyclopedia of distances. Heidelberg: Springer.
Google Scholar
Drton, M., & Schwingenschlögl, U. (2005). Asymptotic seat bias formulae. Metrika,62(1), 23–31. https://doi.org/10.1007/s001840400352.
Article
Google Scholar
Equer, M. (1911). Relation entre la méthode d’Hondt et la proportionnalité. La Grande Revue, Deuxième série,31, 130–137.
Google Scholar
Evci, U. J., & Kaminski, M. M. (2019). Electoral engineering in 2018 Turkish parliamentary elections. Unpublished manuscript in the authors’ possession.
Flis, J., Słomczyński, W., & Stolicki, D. (2019). Seat allocation and seat bias under the Jefferson–D’Hondt System. arXiv: 1805.08291 [physics.soc-ph].
Gfeller, J. (1890). Du transfert des suffrages et de la répartition des sièges complémentaires. Représentation proportionnelle. Revue mensuelle,9, 120–131.
Google Scholar
Gudgin, G., & Taylor, J. P. (1979). Seats, votes, and the spatial organisation of elections. London: Pion.
Google Scholar
Hagenbach-Bischoff, E. (1888). Die Frage der Einführung einer Proportionalvertretung statt des absoluten Mehres. Basel: H. Georg.
Google Scholar
Hagenbach-Bischoff, E. (1905). Die Verteilungsrechnung beim Basler Gesetz nach dem Grundsatz der Verhältniswahl. Basel: Berichthaus.
Google Scholar
Happacher, M., & Pukelsheim, F. (1996). Rounding probabilities: Unbiased multipliers. Statistics & Decisions,14(4), 373–382. https://doi.org/10.1524/strm.1996.14.4.373.
Article
Google Scholar
Happacher, M., & Pukelsheim, F. (2000). Rounding probabilities: Maximum probability and minimum complexity multipliers. Journal of Statistical Planning and Inference,85(1–2), 145–158. https://doi.org/10.1016/S0378-3758(99)00077-4.
Article
Google Scholar
Humphreys, J. H. (1911). Proportional representation: A study in methods of election. London: Methuen & Co.
Google Scholar
Huntington, E. V. (1921). The mathematical theory of the apportionment of representatives. Proceedings of the National Academy of Sciences,7(4), 123–127.
Article
Google Scholar
Huntington, E. V. (1928). The apportionment of representatives in Congress. Transactions of the American Mathematical Society,30(1), 85–110.
Article
Google Scholar
Huntington, E. V. (1931). Methods of apportionment in congress. American Political Science Review,25(4), 961–965. https://doi.org/10.2307/1946616.
Article
Google Scholar
James, E. J. (1897). The first apportionment of federal representatives in the United States. Annals of the American Academy of Political and Social Science,9(1), 1–41.
Article
Google Scholar
Janson, S. (2014). Asymptotic bias of some election methods. Annals of Operations Research,215(1), 89–136. https://doi.org/10.1007/s10479-012-1141-2.
Article
Google Scholar
Jefferson, T. (1792). Opinion on apportionment bill. In Oberg, B., & Looney, J. J. (2008) The papers of Thomas Jefferson, digital edition. Charlottesville: University of Virginia Press.
Joachim, V. (1917). K otázce poměrného zastoupení. Správní obzor,9(8), 289–298.
Google Scholar
Kaminski, M. M. (2001). Coalitional stability of multi-party systems: Evidence from Poland. American Journal of Political Science,45(2), 294–312. https://doi.org/10.2307/2669342.
Article
Google Scholar
Kaminski, M. M. (2002). Do parties benefit from electoral manipulation? Electoral laws and heresthetics in Poland. Journal of Theoretical Politics,14(3), 325–359. https://doi.org/10.1177/095169280201400303.
Article
Google Scholar
Kaminski, M. M. (2018). Spoiler effects in proportional representation systems: Evidence from eight Polish parliamentary elections, 1991–2015. Public Choice,176(3–4), 441–460. https://doi.org/10.1007/s11127-018-0565-x.
Article
Google Scholar
Karpov, A. (2015). Alliance incentives under the D’Hondt method. Mathematical Social Sciences,74(C), 1–7. https://doi.org/10.1016/j.mathsocsci.2014.12.001.
Article
Google Scholar
Katz, J. N., & King, G. (1999). A statistical model for multiparty electoral data. American Political Science Review,93(1), 15–32. https://doi.org/10.2307/2585758.
Article
Google Scholar
Kollman, K., Hicken, A., Caramani, D., Backer, D., & Lublin, D. (2018). Constituency-Level Elections Archive. Ann Arbor: Center for Political Studies, University of Michigan. Available at: http://www.electiondataarchive.org/. Accessed 12 June 2016.
Leutgäb, P., & Pukelsheim, F. (2009). List apparentements in local elections—A lottery. In Holler, M., & Nurmi, H. (Eds.) Power, voting, and voting power: 30 years after (pp. 489–500). Berlin: Springer. https://doi.org/10.1007/978-3-642-35929-3_7.
Chapter
Google Scholar
Li, Y., & Shugart, M. S. (2016). The Seat Product Model of the effective number of parties: A case for applied political science. Electoral Studies,41, 23–43. https://doi.org/10.1016/j.electstud.2015.10.011.
Article
Google Scholar
Lijphart, A. (1990). The political consequences of electoral laws, 1945–85. American Political Science Review,84(2), 481–496. https://doi.org/10.2307/1963530.
Article
Google Scholar
Lijphart, A., & Gibberd, R. W. (1977). Thresholds and payoffs in list systems of proportional representation. European Journal of Political Research,5(3), 219–244. https://doi.org/10.1111/j.1475-6765.1977.tb01289.x.
Article
Google Scholar
Linzer, D. A. (2012). The relationship between seats and votes in multiparty systems. Political Analysis,20(3), 400–416. https://doi.org/10.1093/pan/mps017.
Article
Google Scholar
Marshall, A. W., Olkin, I., & Pukelsheim, F. (2002). A majorization comparison of apportionment methods in proportional representation. Social Choice and Welfare,19(4), 885–900. https://doi.org/10.1007/s003550200164.
Article
Google Scholar
McGhee, E. (2014). Measuring partisan bias in single-member district electoral systems. Legislative Studies Quarterly,39(1), 55–85. https://doi.org/10.1111/lsq.12033.
Article
Google Scholar
McGhee, E. (2017). Measuring efficiency in redistricting. Election Law Journal,16(4), 417–442. https://doi.org/10.1089/elj.2017.0453.
Article
Google Scholar
Mora, X. (2013). La regla de Jefferson–D’Hondt i les seves alternatives. Materials Matemàtics,4, 1–34.
Google Scholar
Morse, M., Von Neumann, J., & Eisenhart, L. P. (1948). Report to the President of the National Academy of Sciences. Washington, DC: National Academy of Sciences.
Google Scholar
Palomares, A., & Ramírez, Gonzáles V. (2003). Thresholds of the divisor methods. Numerical Algorithms,34(2), 405–415. https://doi.org/10.1023/B:NUMA.0000005353.82970.ce.
Article
Google Scholar
Pavia, J., & García-Cárceles, B. (2016). Estimating representatives from election poll proportions: The Spanish case. Statistica Applicata—Italian Journal of Applied Statistics,25(3), 325–340.
Google Scholar
Pólya, G. (1918a). Sur la représentation proportionnelle en matière électorale. L’Enseignement Mathématique,20, 355–379.
Google Scholar
Pólya, G. (1918b). Über die Verteilungssysteme der Proportionalwahl. Zeitschrift für schweizerische Statistik und Volkswirtschaft,54, 363–387.
Google Scholar
Pólya, G. (1919a). Proportionalwahl und wahrscheinlichkeitsrechnung. Zeitschrift für die gesamte Staatswissenschaft,74, 297–322.
Google Scholar
Pólya, G. (1919b). Über die systeme der sitzverteilung bei proportionalwahl. Wissen und Leben—Schweizerische Halbmonatsschrift,12(259–268), 307–312.
Google Scholar
Poptcheva, E. M. (2016). Understanding the D’Hondt method. Allocation of parliamentary seats and leadership positions. European Parliamentary Research Service Briefing PE 580.901, http://www.europarl.europa.eu/RegData/etudes/BRIE/2016/580901/EPRS_BRI(2016)580901_EN.pdf.
Pukelsheim, F. (2014). Proportional representation: Apportionment methods and their applications. Heidelberg: Springer.
Book
Google Scholar
Pukelsheim, F. (2017). Proportional representation: Apportionment methods and their applications (2nd ed.). Heidelberg: Springer.
Book
Google Scholar
Rae, D. W. (1967). The political consequences of electoral laws. New Haven: Yale University Press.
Google Scholar
Rae, D. W., Hanby, V. J., & Loosemore, J. (1971). Thresholds of representation and thresholds of exclusion. An analytic note on electoral systems. Comparative Political Studies,3(4), 479–488. https://doi.org/10.1177/001041407100300406.
Article
Google Scholar
Rokkan, S. (1968). Elections: Electoral systems. In Sills, D. L. (Ed.) International encyclopaedia of the social sciences (Vol. 5, pp. 6–21). New York: Crowell-Collier-Macmillan.
Sainte-Laguë, A. (1910). La représentation proportionnelle et la méthode des moindres carrés. Annales scientifiques de l’École Normale Supérieure, Sér.,3(27), 529–542. https://doi.org/10.24033/asens.627.
Article
Google Scholar
Schuster, K., Pukelsheim, F., Drton, M., & Draper, N. R. (2003). Seat biases of apportionment methods for proportional representation. Electoral Studies,22(4), 651–676. https://doi.org/10.1016/S0261-3794(02)00027-6.
Article
Google Scholar
Shugart, M. S., & Taagepera, R. (2017). Electoral system effects on party systems. In Herron, E., Pekkanen, R., & Shugart, M. S. (Eds.) Oxford handbook of electoral systems (pp. 41–68). New York: Oxford. https://doi.org/10.1093/oxfordhb/9780190258658.001.0001.
Google Scholar
Shugart, M. S., & Taagepera, R. (2017b). Votes from seats: Logical models of electoral systems. Cambridge: Cambridge University Press.
Book
Google Scholar
Stephanopoulos, N. O., & McGhee, E. M. (2015). Partisan gerrymandering and the efficiency gap. University of Chicago Law Review,82(2), 831–900.
Google Scholar
Stephanopoulos, N. O., & McGhee, E. M. (2018). The measure of a metric: The debate over quantifying partisan gerrymandering. Stanford Law Review,70(5), 1503–1568.
Google Scholar
Szpiro, G. G. (2010). Numbers rule: The vexing mathematics of democracy, from Plato to the present. Princeton: Princeton University Press.
Book
Google Scholar
Taagepera, R. (1986). Reformulating the cube law for proportional representation elections. American Political Science Review,80(2), 489–504. https://doi.org/10.2307/1958270.
Article
Google Scholar
Taagepera, R. (2007). Predicting party sizes: The logic of simple electoral systems. Oxford: Oxford University Press.
Book
Google Scholar
Taagepera, R., & Laakso, M. (1980). Proportionality profiles of West European electoral systems. European Journal of Political Research,8(4), 423–446. https://doi.org/10.1111/j.1475-6765.1980.tb00582.x.
Article
Google Scholar
Taagepera, R., & Shugart, M. S. (1989). Seats and votes: The effects and determinants of electoral systems. New Haven: Yale University Press.
Google Scholar
Tapp, K. (2018). Measuring political gerrymandering. arXiv: 1801.02541 [physics.soc-ph].
Udina, F., & Delicado, P. (2005). Estimating parliamentary composition through electoral polls. Journal of the Royal Statistical Society. Series A (Statistics in Society),168(2), 387–399.
Article
Google Scholar
Veomett, E. (2018). The efficiency gap, voter turnout, and the efficiency principle. arXiv: 1801.05301 [physics.soc-ph].