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Multidimensional Spatial Voting with Non-separable Preferences

Published online by Cambridge University Press:  04 January 2017

Lukas F. Stoetzer  and
Steffen Zittlau
Lukas F. Stoetzer
Affiliation:
Department of Political Science, University of Mannheim. e-mail: lstoetze@mail.uni-mannheim.de
Steffen Zittlau*
Affiliation:
Department of Political Science, University of Mannheim
*
e-mail: zittlau@uni-mannheim.de (corresponding author)
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Abstract

In most multidimensional spatial models, the systematic component of agent utility functions is specified as additive separable. We argue that this assumption is too restrictive, at least in the context of spatial voting in mass elections. Here, assuming separability would stipulate that voters do not care about how policy platforms combine positions on multiple policy dimensions. We present a statistical implementation of Davis, Hinich, and Ordeshook's (1970) Weighted Euclidean Distance model that allows for the estimation of the direction and magnitude of non-separability from vote choice data. We demonstrate in a Monte-Carlo experiment that conventional separable model specifications yield biased and/or unreliable estimates of the effect of policy distances on vote choice probabilities in the presence of non-separable preferences. In three empirical applications, we find voter preferences on economic and socio-cultural issues to be non-separable. If non-separability is unaccounted for, researchers run the risk of missing crucial parts of the story. The implications of our findings carry over to other fields of research: checking for non-separability is an essential part of robustness testing in empirical applications of multidimensional spatial models.

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Type
Articles
Information
Political Analysis , Volume 23 , Issue 3 , Summer 2015 , pp. 415 - 428
Copyright
Copyright © The Author 2015. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors’ note: The order of authors’ names reflects alphabetical convention. Both authors have contributed equally to all work. For helpful comments and suggestions, we thank two anonymous reviewers, R. Michael Alvarez, Thomas Gschwend, Thomas Bräuninger, Max Alletse, Catherine de Vries, Franz Urban Pappi, Sean Carey, Caroline Wittig and all participants of the CDSS doctoral workshop. All errors remain our own. Replication files for this article are available at http://dx.doi.org/10.7910/DVN/VCSRMX. Supplementary Materials for this article are available on the Political Analysis Web site.

References

Aldrich, J. H., and McKelvey, R. D. 1977. A method of scaling with applications to the 1968 and 1972 presidential elections. American Political Science Review 71(1): 111–30.Google Scholar
Aldrich, J. H., Montgomery, J. M., and Sparks, D. B. 2014. Polarization and ideology: Partisan sources of low dimensionality in scaled roll call analyses. Political Analysis 22(4): 435–56.Google Scholar
Alvarez, R. M., and Nagler, J. 1998. When politics and models collide: Estimating models of multiparty elections. American Journal of Political Science 42(1): 55–96.Google Scholar
Alvarez, R. M., and Nagler, J. 2004. Party system compactness: Measurement and consequences. Political Analysis 12(1): 46–62.Google Scholar
American National Election Studies. 2009. American National Election Studies (ANES) Panel Study, 2008–2009. ICPSR29182-V1. http://doi.org/10.3886/ICPSR29182.v1.Google Scholar
Bartels, L. M. 2006. What's the matter with what's the matter with Kansas? Quarterly Journal of Political Science 1(2): 201–26.Google Scholar
Benoit, J.-P., and Kornhauser, L. A. 1994. Social choice in a representative democracy. American Political Science Review 88(1): 185–92.Google Scholar
Benoit, K., and Laver, M. 2006. Party policy in modern democracies. London: Routledge.Google Scholar
Brams, S. J., Kilgour, D. M., and Zwicker, W. S. 1997. Voting on referenda: The separability problem and possible solutions. Electoral Studies 16(3): 359–77.Google Scholar
Brams, S. J., Kilgour, D. M., and Zwicker, W. S. 1998. The paradox of multiple elections. Social Choice and Welfare 15(2): 211–36.Google Scholar
Calvert, R. L. 1985. Robustness of the multidimensional voting model: Candidate motivations, uncertainty, and convergence. American Journal of Political Science 29(1): 69–95.Google Scholar
Clinton, J., Jackman, S., and Rivers, D. 2004. The statistical analysis of roll call data. American Political Science Review 98(2): 1–16.Google Scholar
Commission of the European Communities. 2012. Eurobarometer 11 (April 1979). http://dx.doi.Org/10.4232/l.10866.Google Scholar
Converse, P. E. 1964. The nature of belief systems in mass publics. In Ideology and discontent, ed. Apter, D., 206–61. New York: Free Press.Google Scholar
Cox, G. W. 1984. Electoral equilibrium in double member districts. Public Choice 44(3): 443–51.Google Scholar
Davis, O. A., Hinich, M. J., and Ordeshook, P. C. 1970. An expository development of a mathematical model of the electoral process. American Political Science Review 64(2): 426–48.Google Scholar
De Vries, C. E., van der Brug, W., van Egmond, M. H., and van der Eijk, C. 2011. Individual and contextual variation in EU issue voting: The role of political information. Electoral Studies 30(1): 16–28.Google Scholar
Denzau, A. T., and Mackay, R. J. 1981. Structure-induced equilibria and perfect-foresight expectations. American Journal of Political Science 25(4): 762–79.Google Scholar
Dow, J. K., and Endersby, J. W. 2004. Multinomial probit and multinomial logit: A comparison of choice models for voting research. Electoral Studies 23(1): 107–22.Google Scholar
Downs, A. 1957. An Economic Theory of Democracy. New York: Harper.Google Scholar
Enelow, J. M., and Hinich, M. J. 1984. The spatial theory of voting: An introduction. New York: Cambridge University Press.Google Scholar
Finke, D. 2009. Estimating the effect of nonseparable preferences in EU treaty negotiations. Journal of Theoretical Politics 21(4): 543–69.Google Scholar
Finke, D., and Fleig, A. 2013. The merits of adding complexity: Non-separable preferences in spatial models of European Union politics. Journal of Theoretical Politics 25(4): 546–75.Google Scholar
Fiorina, M. P., Abrams, S. A., and Pope, J. C. 2008. Polarization in the American public: Misconceptions and misreadings. Journal of Politics 70(2): 556–60.Google Scholar
Gelman, A. 2008. Red state, blue state, rich state, poor state: Why Americans vote the way they do. Princeton, NJ: Princeton University Press.Google Scholar
Herron, M. 1999. Post-estimation uncertainty in limited dependent variables models. Political Analysis 8(1): 83–98.Google Scholar
Hinich, M. J., and Munger, M. C. 1997. Analytical politics. Cambridge: Cambridge University Press.Google Scholar
Hobolt, S. B., Spoon, J.-J., and Tilley, J. 2009. A vote against Europe? Explaining defection at the 1999 and 2004 European parliament elections. British Journal of Political Science 39(01): 93–115.Google Scholar
Jessee, S. A. 2009. Spatial voting in the 2004 presidential election. American Political Science Review 103(01): 59–81.Google Scholar
Kadane, J. B. 1972. On division of the question. Public Choice 13(1): 47–54.Google Scholar
Kedar, O. 2005. When moderate voters prefer extreme parties: Policy balancing in parliamentary elections. American Political Science Review 99(2): 185–99.Google Scholar
Klar, S. 2014. A multidimensional study of ideological preferences and priorities among the American public. Public Opinion Quarterly 78:344–59.Google Scholar
Kramer, G. H. 1972. Sophisticated voting over multidimensional choice spaces. Journal of Mathematical Sociology 2(2): 165–80.Google Scholar
Lacy, D. 2001a. A theory of nonseparable preferences in survey responses. American Journal of Political Science 45(2): 239–58.Google Scholar
Lacy, D. 2001b. Nonseparable preferences, measurement error, and unstable survey responses. Political Analysis 9(2): 95–115.Google Scholar
Lacy, D., and Niou, E. M. 2000. A problem with referendums. Journal of Theoretical Politics 12(1): 5–31.Google Scholar
Lacy, D., and Niou, E. M. S. 1998. Elections in double-member districts with nonseparable voter preferences. Journal of Theoretical Politics 10(1): 89–110.Google Scholar
Lee, L.-f. 1980. Specification error in multinomial logit models: Analysis of the omitted variable bias. Discussion Paper No. 80–131. Center for Economic Research, University of Minnesota.Google Scholar
Levendusky, M. S. 2009. The microfoundations of mass polarization. Political Analysis 17(2): 162–76.Google Scholar
Lin, T.-M., Enelow, J. M., and Dorussen, H. 1999. Equilibrium in multicandidate probabilistic spatial voting. Public Choice 98(1–2): 59–82.Google Scholar
Lo, J., Proksch, S.-O., and Gschwend, T. 2013. A common left-right scale for voters and parties in Europe. Political Analysis 22(2): 205–23.Google Scholar
Mackay, R. J., and Weaver, C. L. 1981. Agenda control by budget maximizers in a multi-bureau setting. Public Choice 37(3): 447–72.Google Scholar
McFadden, D. 1974. Conditional Logit analysis of qualitative choice behavior. In Frontiers in Econometrics, ed. Zarembka, P., 105–42. New York: Academic Press.Google Scholar
McCarty, N., Poole, K. T., and Rosenthal, H. 2006. Polarized America: The dance of ideology and unequal riches. Cambridge, MA: MIT Press.Google Scholar
McKelvey, R. D. 1986. Covering, dominance, and institution-free properties of social choice. American Journal of Political Science 30(2): 283–314.Google Scholar
Merrill, S., and Adams, J. 2001. Computing Nash equilibria in probabilistic, multiparty spatial models with nonpolicy components. Political Analysis 9(4): 347–61.Google Scholar
Milyo, J. 2000. Logical deficiencies in spatial models: A constructive critique. Public Choice 105(3–4): 273–89.Google Scholar
Ordeshook, P. C. 1986. Game theory and political theory. New York: Cambridge University Press.Google Scholar
Pinheiro, J. C., and Bates, D. M. 1996. Unconstrained parametrizations for variance-covariance matrices. Statistics and Computing 6(3): 289–96.Google Scholar
Poole, K. T., and Rosenthal, H. 1985. A spatial model for legislative roll call analysis. American Journal of Political Science 29(2): 357–84.Google Scholar
Poole, K. T., and Rosenthal, H. 2007. Ideology & Congress. New Brunswick, NJ: Transaction Publishers.Google Scholar
Quinn, K. M., Martin, A. D., and Whitford, A. B. 1999. Voter choice in multi-party democracies: A test of competing theories and models. American Journal of Political Science 43(4): 1231–47.Google Scholar
Rivers, D. 1988. Heterogeneity in models of electoral choice. American Journal of Political Science 32(3): 737–57.Google Scholar
Schofield, N. 1978. Instability of simple dynamic games. Review of Economic Studies 45(3): 575–94.Google Scholar
Schofield, N., Martin, A. D., Quinn, K. M., and Whitford, A. B. 1998. Multiparty electoral competition in the Netherlands and Germany: A model based on multinomial probit. Public Choice 97(2): 257–93.Google Scholar
Schofield, N., and Sened, I. 2005. Multiparty competition in Israel, 1988–96. British Journal of Political Science 35(4):635.Google Scholar
Schofield, N., and Zakharov, A. 2009. A stochastic model of the 2007 Russian Duma election. Public Choice 142(1–2): 177–94.Google Scholar
Schwartz, T. 1977. Collective choice, separation of issues and vote trading. American Political Science Review 71(3): 999–1010.Google Scholar
Shafer, B. E., and Claggett, W. J. M. 1995. The two majorities: The issue context of American politics. Baltimore: Johns Hopkins University Press.Google Scholar
Shikano, S. 2008. Die Eigendynamik zur Eindimensionalität des Parteienwettbewerbs: Eine Simulationsstudie. Politische Vierteljahresschrift 49(2): 229–50.Google Scholar
Signorino, C. S., and Yilmaz, K. 2003. Strategic misspecification in regression models. American Journal of Political Science 47(3): 551–66.Google Scholar
Treier, S., and Hillygus, D. S. 2009. The nature of political ideology in the contemporary electorate. Public Opinion Quarterly 73(4): 679–703.Google Scholar
van Egmond, M., van der Brug, W., Hobolt, S., Franklin, M., and Sapir, E. V. 2013. European parliament election study 2009, voter study. http://dx.doi.Org/10.4232/l.11760.Google Scholar
Wooldridge, J. M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.Google Scholar
Yatchew, A., and Griliches, Z. 1985. Specification error in probit models. Review of Economics and Statistics 67(1): 134–39.Google Scholar
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