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A Statistical Model for Party-Systems Analysis

  • Arturas Rozenas (a1) and R. Michael Alvarez (a1)


Empirical researchers studying party systems often struggle with the question of how to count parties. Indexes of party system fragmentation used to address this problem (e.g., the effective number of parties) have a fundamental shortcoming: since the same index value may represent very different party systems, they are impossible to interpret and may lead to erroneous inference. We offer a novel approach to this problem: instead of focusing on index measures, we develop a model that predicts the entire distribution of party vote-shares and, thus, does not require any index measure. First, a model of party counts predicts the number of parties. Second, a set of multivariate t models predicts party vote-shares. Compared to the standard index-based approach, our approach helps to avoid inferential errors and, in addition, yields a much richer set of insights into the variation of party systems. For illustration, we apply the model on two data sets. Our analyses call into question the conclusions one would arrive at by the index-based approach. Software is provided to implement the proposed model.



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Aitchison, Jim. 1982. The statistical analysis of compositional data. Journal of the Royal Statistical Society, Series B (Methodological) 44: 139–77.
Alvarez, Michael R., and Nagler, Jonathan. 2004. Party system compactness: Measurement and consequences. Political Analysis 12: 4662.
Bogaards, Matthijs. 2004. Counting parties and identifying dominant party systems in Africa. European Journal of Political Research 43: 173–97.
Butler, Adam, and Glasbey, Chris. 2008. A latent Gaussian model for compositional data with zeros. Journal of the Royal Statistical Society 57: 505–20.
Clark, William Roberts, and Golder, Matt. 2006. Rehabilitating Duverger's theory. Comparative Political Studies 39: 679708.
Cox, Gary W. 1997. Making votes count. Cambridge: Cambridge University Press.
de Palma, A., Hong, Gap-Seon, and Thisse, J. F. 1990. Equilibria in multi-party competition under uncertainty. Social Choice and Welfare 7: 247–59.
Dunleavy, Patrick and Boucek, Françoise. 2003. Constructing the mumber of parties. Party Politics 9: 291315.
Duverger, Maurice. 1954. Political parties. New York: Wiley.
Gelman, Andrew, Carlin, John B., Stern, Hal B., and Rubin, Donald B. 2003. Bayesian data analysis. 2nd ed. London: Chapman and Hall.
Golosov, Grigorii V. 2010. The effective number of parties. Party Politics 16: 171–92.
Grofman, Bernard, Bowler, Shaun, and Blais, Andre. 2009. Introduction: Evidence for Duverger's law from four countries. In Duverger's law of plurality voting, eds. Grofman, Bernard, Blais, Andre, and Bowler, Shaun, 111. New York: Springer.
Gross, Donald A., and Sigelman, Lee. 1984. Comparing party systems: A multidimensional approach. Comparative Politics 16: 463–79.
Honaker, James, Katz, Jonathan, and King, Gary. 2002. A fast, easy, and efficient estimator for multiparty electoral data. Political Analysis 10: 84100.
Jackson, John E. 2002. A seemingly unrelated regression model for analyzing multiparty elections. Political Analysis 10: 4965.
Katz, Jonathan N., and King, Gary. 1999. A statistical model for multiparty electoral data. American Political Science Review 93(1): 1532.
Laakso, Markku, and Taagepera, Rein. 1979. Effective number of parties: A measure with application to West Europe. Comparative Political Studies 12: 327.
Lipset, Seymour Martin, and Rokkan, Stein. 1967. Cleavage stuctures, party systems and voter alignments: An introduction. In Party systems and voter alignments: Cross-national perspectives, eds. Lipset, S. M. and Rokkan, Stein. New York: Free Press.
Liu, Chuanhai. 1996. Bayesian robust multivariate linear regression with incomplete data. Journal of the American Statistical Association 91: 1219–27.
Molinar, Juan. 1991. Counting the number of parties: An alternative index. American Political Science Review 85: 1383–91.
Mustillo, Thomas J. 2009. Modeling new party performance: A conceptual and methodological approach for volatile party systems. Political Analysis 17: 311–32.
Myerson, Roger B., and Weber, Robert J. 1993. A theory of voting equilibria. American Political Science Review 87: 102–14.
Ordeshook, Peter C., and Shvetsova, Olga V. 1994. Ethnic heterogeneity, district magnitude, and the number of parties. American Journal of Political Science 38: 100–23.
Osborne, Martin J., and Tourky, Rabee. 2008. Party formation in single-issue politics. Journal of the European Economic Association 6: 9741005.
Rae, Douglas W. 1967. The political consequences of electoral laws. New Haven, CT: Yale University.
Reed, Steven R. n.d. Japan MMD data set.∼sreed/DataPage.html.
Rehm, Phillip, and Reilly, Timothy. 2010. United we stand: Constituency homogeneity and comparative party polarization. Electoral Studies 29: 4053.
Riker, William. 1982. The two-party system and Duverger's law: An essay on the history of political science. American Political Science Review 76: 733–66.
Sartori, Giovani. 1976. Parties and party systems. A framework for analysis. Cambridge: Cambridge University Press.
Selway, Joel S. 2011. The measurement of cross-cutting cleavages and other multidimensional cleavage structures. Political Analysis 19: 4865.
Tomz, Michael, Tucker, Joshua A., and Wittenberg, Jason. 2002. An easy and accurate regression model for multiparty electoral data. Political Analysis 10: 6683.
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A Statistical Model for Party-Systems Analysis

  • Arturas Rozenas (a1) and R. Michael Alvarez (a1)


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