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National Electoral Thresholds and Disproportionality

Published online by Cambridge University Press:  13 July 2020

Tasos Kalandrakis Open the ORCID record for Tasos Kalandrakis [Opens in a new window]  and
Miguel R. Rueda Open the ORCID record for Miguel R. Rueda [Opens in a new window]
Tasos Kalandrakis*
Affiliation:
Department of Political Science and Department of Economics, University of Rochester, Rochester, NY14627, USA. Email: kalandrakis@rochester.edu
Miguel R. Rueda
Affiliation:
Department of Political Science, Emory University, Atlanta, GA30322, USA. Email: miguel.rueda@emory.edu
*
*Email: kalandrakis@rochester.edu
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Abstract

We model the conditional distribution of seats given vote shares induced by national electoral systems using a stochastic threshold of representation and a disproportionality parameter that regulates allocation for parties above the threshold. We establish conditions for the parameters of this model to be identified from observed seats/votes data, and develop a Maximum a Posteriori Expectation-Maximization (MAP-EM) algorithm to estimate them. We apply the procedure to 116 electoral systems used in 417 elections to the lower house across 36 European countries since WWII. We reject a test of model fit in only 5 of those systems, while a simpler model without thresholds is rejected in favor of our estimated model in 49 electoral systems. We find that the two modal electoral system configurations involve higher thresholds with seat allocation for parties exceeding thresholds that does not statistically differ from perfectly proportional allocation (32.76% of all systems); and systems for which we cannot reject the absence of a national threshold but exhibit disproportional seat allocation for parties eligible for seats (38.79% of all systems). We also develop procedures to test for significant changes in electoral institutions and/or the distribution of seats.

Keywords

electoral thresholdselectoral disproportionalityMAP-EM algorithm
Type
Articles
Information
Political Analysis , Volume 29 , Issue 1 , January 2021 , pp. 102 - 119
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology.

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Footnotes

Contributing Editor: Jeff Gill

References

Alvarez-Rivera, M.2011. “Election Resources on the Internet.” http://electionresources.org/.Google Scholar
Andrews, D. W. K. 2001. “Testing When a Parameter Is on the Boundary of the Maintained Hypothesis.” Econometrica 69:683–734.CrossRefGoogle Scholar
Beck, T., Clarke, G., Groff, A., Keefer, P., and Walsh, P.. 2001. “New Tools and New Tests in Comparative Political Economy: The Database of Political Institutions.” World Bank Economic Review 15:165–176.CrossRefGoogle Scholar
Calvo, E. 2009. “The Competitive Road to Proportional Representation: Partisan Biases and Electoral Regime Change Under Increasing Party Competition.” World Politics 61(2):254–295.CrossRefGoogle Scholar
Calvo, E., and Rodden, J.. 2015. “The Achilles Heel of Plurality Systems: Geography and Representation in Multiparty Democracies.” American Journal of Political Science 59(4):789–805.CrossRefGoogle Scholar
Caramani, D. 2000. Elections in Western Europe Since 1815: Electoral Results by Constituencies . London: Macmillan Reference.CrossRefGoogle Scholar
Carr, A.2011. “Psephos Adam Carr’s Election Archive.” http://psephos.adam-carr.net/.Google Scholar
Carstairs, A. M. 1980. A Short History of Electoral Systems in Western Europe . London: Allen & Unwin.Google Scholar
Cox, G. 1997. Making Votes Count . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Cox, G., and Shugart, M. S.. 1991. “Comment on Gallagher’s ‘Proportionality, Disproportionality, and Electoral Systems’.” Electoral Studies 10(4):348–352.CrossRefGoogle Scholar
Dempster, A. P., Laird, N. M., and Rubin, D. B.. 1977. “Maximum Likelihood from Incomplete Data via the EM Algorithm.” Journal of the Royal Statistical Society. Series B (Methodological) 39(1):1–38.CrossRefGoogle Scholar
European Commission for Democracy through law (Venice Commission). 2018. Compilation of Venice Commission Opinions and Reports Concerning Thresholds that bar Parties from Access to Parliament. 004 Council of Europe https://www.venice.coe.int/webforms/documents/?pdf=CDL-PI(2018)004-e:.Google Scholar
Fraley, C., and Raftery, A.. 2007. “Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering.” Journal of Classification 24:155–181.CrossRefGoogle Scholar
Gallagher, M. 1991. “Proportionality, Disproportionality, and Electoral Systems.” Electoral Studies 10(1):33–51.CrossRefGoogle Scholar
Gallagher, M. 1992. “Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities.” British Journal of Political Science 22(4):469–496.CrossRefGoogle Scholar
Gelman, A., and King, G.. 1990. “Estimating the Electoral Consequences of Legislative Redistricting.” Journal of the American Statistical Association 85:274–282.CrossRefGoogle Scholar
Gelman, A., and King, G.. 1994. “Enhancing Democracy Through Legislative Redistricting.” American Political Science Review 88:541–559, Parts reprinted in California Policy Studies Brief, a publication of the California Policy Seminar, Vol. 7, No. 5 (April, 1995).CrossRefGoogle Scholar
Golder, M. 2006. “Democratic Electoral Systems around the World, 1946–2000.” Electoral Studies 24:103–121.CrossRefGoogle Scholar
Grofman, B. 1983. “Measures of Bias and Proportionality in Seats-Votes Relationships.” Political Methodology 9:295–327.Google Scholar
Inter-Parliamentary Union. 2011. “PARLINE Database on National Parliaments.” http://www.ipu.org/parline-e/parlinesearch.asp.Google Scholar
Jackman, S. 1994. “Measuring Electoral Bias: Australia 1949–93.” British Journal of Political Science 24(3):319–357.CrossRefGoogle Scholar
Kalandrakis, T., and Rueda, M. R.. 2020. “Replication Data for: National Electoral Thresholds and Disproportionality.” https://doi.org/10.7910/DVN/E6NN9E, Harvard Dataverse, V1.CrossRefGoogle Scholar
Kendall, M. G., and Stuart, A.. 1950. “The Law of the Cubic Proportion in Election Results.” The British Journal of Sociology 1(3):183–196.CrossRefGoogle Scholar
King, G. 1990. “Electoral Responsiveness and Partisan Bias in Multiparty Democracies.” Legislative Studies Quarterly 15(2):159–181.CrossRefGoogle Scholar
King, G., and Browning, R. X.. 1987. “Democratic Representation and Partisan Bias in Congressional Elections.” American Political Science Review 81(4):1251–1273.CrossRefGoogle Scholar
Levitan, E., and Herman, G. T.. 1987. “A Maximum A Posteriori Probability Expectation Maximization Algorithm for Image Reconstruction in Emission Tomography.” IEEE Transactions on Medical Imaging MI‐6(3):185–192.CrossRefGoogle Scholar
Lijphart, A. 1994. Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945–1990 . Oxford: Oxford University Press.CrossRefGoogle Scholar
Linzer, D. A. 2012. “The Relationship between Seats and Votes in Multiparty Systems.” Political Analysis 20(3):400.CrossRefGoogle Scholar
Mackie, T., and Rose, R.. 1991. The International Almanac of Electoral History . London: Macmillan.CrossRefGoogle Scholar
Nohlen, D., and Stöver, P.. 2010. Elections in Europe: A Data Handbook . Baden-Baden: Nomos.CrossRefGoogle Scholar
Norwegian Social Science Data Services. 2011. “European Election Database.” http://www.nsd.uib.no/european_election_database/.Google Scholar
Renwick, A. 2010. The Politics of Electoral Reform . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Ruiz-Rufino, R. 2007. “Aggregated Threshold Functions or How to Measure the Performance of an Electoral System.” Electoral Studies 26:492–502.CrossRefGoogle Scholar
Schrodt, P. A. 1981. “A Statistical Study of the Cube Law in Five Electoral Systems.” Political Methodology 7(2):31–53.Google Scholar
Taagepera, R. 1973. “Seats and Votes: A Generalization of the Cube Law of Elections.” Social Science Research 2:257–275.CrossRefGoogle Scholar
Taagepera, R. 1986. “Reformulating the Cube Law for Proportional Representation Elections.” American Political Science Review 80(2):489–504.CrossRefGoogle Scholar
Taagepera, R. 1989. “Empirical Threshold of Representation.” Electoral Studies 8(2):105–116.CrossRefGoogle Scholar
Taagepera, R. 1998a. “Effective Magnitude and Effective Threshold.” Electoral Studies 17(4):393–404.Google Scholar
Taagepera, R. 1998b. “Nationwide Inclusion and Exclusion Thresholds of Representation.” Electoral Studies 17(4):405–417.CrossRefGoogle Scholar
Taagepera, R. 2002. “Nationwide Threshold of Representation.” Electoral Studies 21(3):383–401.CrossRefGoogle Scholar
Taagepera, R., and Shugart, M. S.. 1989. Seats and Votes: The Effects and Determinants of Electoral Systems . Yale University Press.Google Scholar
Taagepera, R., and Shugart, M. S.. 2017. Votes from Seats: Logical Models of Electoral Systems . Cambridge: Cambridge University Press.Google Scholar
Theil, H. 1969. “The Desired Political Entropy.” American Political Science Review 63(2):521–525.CrossRefGoogle Scholar
Tufte, E. 1973. “The Relationship Between Seats and Votes in Two-Party Systems.” American Political Science Review 67(2):540–554.CrossRefGoogle Scholar
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