Hostname: page-component-546b4f848f-q5mmw Total loading time: 0 Render date: 2023-06-01T00:30:24.530Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false
  • English

A New Measure of Congruence: The Earth Mover’s Distance

Published online by Cambridge University Press:  22 February 2017

Noam Lupu ,
Lucía Selios  and
Zach Warner
Noam Lupu*
Affiliation:
Department of Political Science, Vanderbilt University, Nashville, TN 37203, USA. Email: noam.lupu@vanderbilt.edu
Lucía Selios
Affiliation:
Instituto de Ciencia Política, Universidad de la República, Montevideo 11200, Uruguay. Email: lucia.selios@cienciassociales.edu.uy
Zach Warner
Affiliation:
Department of Political Science, University of Wisconsin–Madison, Madison, WI 53706, USA. Email: zwarner@wisc.edu
*
*Email: noam.lupu@vanderbilt.edu
Get access Rights & Permissions[Opens in a new window]

Abstract

Scholars of representation are increasingly interested in mass–elite congruence—the degree to which the preferences of elected elites mirror those of voters. Yet existing measures of congruence can be misleading because they ignore information in the data, require arbitrary decisions about quantization, and limit researchers to comparing masses and elites on a single dimension. We introduce a new measure of congruence—borrowed from computer science—that addresses all of these problems: the Earth Mover’s Distance (EMD). We demonstrate its conceptual advantages and apply it to two debates in research on mass–elite congruence: ideological congruence in majoritarian and proportional systems and the determinants of congruence across countries in Latin America. We find that improving measurement using the EMD has important implications for inferences regarding both empirical debates. Even beyond studies of congruence, the EMD is a useful and reliable way for political scientists to compare distributions.

Type
Articles
Information
Political Analysis , Volume 25 , Issue 1 , January 2017 , pp. 95 - 113
Copyright
Copyright © The Author(s) 2017. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Authors’ note: We are grateful to Manuel Alcántara, Matt Golder, and Juan Andrés Moraes for generously sharing their data, and to Andy Eggers, Alicia Fernández, Scott Gehlbach, Álvaro Gómez, Luis Schiumerini, Alex Tahk, Simon Urbanek, and seminar participants at Oxford and Wisconsin for helpful feedback. Previous versions of this paper were presented at the annual meetings of the European Political Science Association, Political Methodology Specialist Group of the Political Studies Association, and Society for Political Methodology. For replication materials, see Lupu, Selios, and Warner (2016). Supplementary materials are available in an online appendix on the Political Analysis website.

Contributing Editor: Jonathan Katz

References

Aggarwal, C. C., Hinneburg, A., and Keim, D. A.. 2001. On the surprising behavior of distance metrics in high dimensional space. In Database theory—ICDT 2001 , ed. Van den Bussche, J. and Vianu, V.. Berlin: Springer, vol. 1973, pp. 420–434.CrossRefGoogle Scholar
Alon, N., Cosares, S., Hochbaum, D. S., and Shamir, R.. 1989. An algorithm for the detection and construction of monge sequences. Linear Algebra and its Applications 114‐115:669–680.CrossRefGoogle Scholar
Andeweg, R. B. 2011. Approaching perfect policy congruence: measurement, development, and relevance for political representation. In How democracy works: political representation and policy congruence in modern societies , ed. Rosema, M., Denters, B., and Aarts, K.. Amsterdam: Amsterdam University Press, pp. 39–52.CrossRefGoogle Scholar
Baldwin, K., and Huber, J. D.. 2010. Economic versus cultural differences: forms of ethnic diversity and public goods provision. American Political Science Review 104(4):644–662.CrossRefGoogle Scholar
Bartels, L. M. 2008. Unequal democracy . Princeton, NJ: Princeton University Press.Google Scholar
Beck, T., Clarke, G., Groff, A., Keefer, P., and Walsh, P.. 2001. New tools in comparative political economy: the database of political institutions. World Bank Economic Review 15(1):165–176.CrossRefGoogle Scholar
Bellman, R. E. 2010. Dynamic programming . Princeton, NJ: Princeton University Press.Google Scholar
Blais, A., and Bodet, M. A.. 2006. Does proportional representation foster closer congruence between citizens and policy makers? Comparative Political Studies 39(10):1243–1262.CrossRefGoogle Scholar
Bormann, N.-C., and Golder, M.. 2013. Democratic electoral systems around the world, 1946-2011. Electoral Studies 32(2):360–369.CrossRefGoogle Scholar
Bornschier, S. 2013. Trayectorias históricas y responsiveness del sistema de partidos en siete países de América Latina. América Latina Hoy 65:45–77.CrossRefGoogle Scholar
Breunig, C., and Jones, B. D.. 2011. Stochastic process methods with an application to budgetary data. Political Analysis 19(1):103–117.CrossRefGoogle Scholar
Budge, I., and McDonald, M. D.. 2007. Election and party system effects on policy representation: bringing time into a comparative perspective. Electoral Studies 26(1):168–179.CrossRefGoogle Scholar
Buquet, D., and Selios, L.. 2017. Political congruence in Uruguay, 2014. ed. Joignant, A., Morales, M., and Fuentes, C.. Malaise in representation in Latin American Countries: Chile, Argentina, Uruguay . New York: Palgrave Macmillan, pp. 187–210.CrossRefGoogle Scholar
Calvo, E., and Murillo, M. V.. 2013. When parties meet voters: assessing political linkages through partisan networks and distributive expectations in argentina and chile. Comparative Political Studies 46(7):851–882.CrossRefGoogle Scholar
Canes-Wrone, B. 2015. From mass preferences to policy. Annual Review of Political Science 18(1):147–165.CrossRefGoogle Scholar
Converse, P. E., and Pierce, R.. 1986. Political representation in France . Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Dalton, R. J. 1985. Political parties and political representation: Party supporters and party elites in nine nations. Comparative Political Studies 18(3):267–299.CrossRefGoogle Scholar
Deza, E., and Deza, M.-M.. 2006. Dictionary of distances . Amsterdam: Elsevier.Google Scholar
Ezrow, L. 2007. The variance matters: How party systems represent the preferences of voters. Journal of Politics 69(1):182–192.CrossRefGoogle Scholar
Ferland, B. 2016. Revisiting the ideological congruence controversy. European Journal of Political Research 55(2):358–373.CrossRefGoogle Scholar
Fiorina, M. P., and Abrams, S. J.. 2008. Political polarization in the american public. Annual Review of Political Science 11(1):563–588.CrossRefGoogle Scholar
Gandrud, C.2015. Gallagher Electoral Disproportionality Data. Available at http://bit.ly/Ss6zDO, last updated 20-MAR-2015. Accessed 21-MAR-2016.Google Scholar
Gilens, M. 2012. Affluence and influence . Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Golder, M., and Lloyd, G.. 2014. Re-evaluating the relationship between electoral rules and ideological congruence. European Journal of Political Research 53(1):200–212.CrossRefGoogle Scholar
Golder, M., and Stramski, J.. 2010. Ideological congruence and electoral institutions: conceptualization and measurement. American Journal of Political Science 54(1):90–106.CrossRefGoogle Scholar
Huber, J. D., and Powell, G. B.. 1994. Congruence between citizens and policymakers in two visions of liberal democracy. World Politics 46(3):291–326.CrossRefGoogle Scholar
Joignant, A., Fuentes, C., and Morales, M., eds. 2017. Malaise in representation in Latin American Countries: Chile, Argentina, Uruguay . New York: Palgrave Macmillan.CrossRefGoogle Scholar
Kitschelt, H., Hawkins, K. A., Luna, J. P., Rosas, G., and Zechmeister, E. J.. 2010. Latin American party systems . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Levina, E., and Bickel, P.. 2001. The Earth mover’s distance is the mallows distance: some insights from statistics. Proceedings of ICCV 2001 , pp. 251–256.Google Scholar
Ling, H., and Okada, K.. 2007. An efficient Earth mover’s distance algorithm for robust histogram comparison. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(5):840–853.CrossRefGoogle ScholarPubMed
Luna, J. P. 2014. Segmented representation: political parties in unequal democracies . Oxford: Oxford University Press.CrossRefGoogle Scholar
Luna, J. P., and Zechmeister, E. J.. 2005. Political representation in latin america: a study of elite-mass congruence in nine countries. Comparative Political Studies 38(4):388–416.CrossRefGoogle Scholar
Lupu, N. 2016. Party brands in crisis: partisanship, brand dilution, and the breakdown of political parties in Latin America . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lupu, N., Selios, L., and Warner, Z.. 2016. Replication Data for: A New measure of Congruence: The Earth Mover’s Distance. https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/NO90AJ, Harvard Dataverse.CrossRefGoogle Scholar
Lupu, N., and Warner, Z.. 2017. Mass-elite congruence and representation in Argentina. ed. Joignant, A., Morales, M., and Fuentes, C.. Malaise in representation in Latin American Countries: Chile, Argentina, Uruguay . New York: Palgrave Macmillan, pp. 281–302.CrossRefGoogle Scholar
Mainwaring, S., Bejarano, A. M., and Pizarro Leongómez, E., eds. 2006. The crisis of demcoratic representation in the Andes . Palo Alto, CA: Stanford University Press.CrossRefGoogle Scholar
Mainwaring, S., and Scully, T. R., eds. 1995. Building democratic institutions: party systems in Latin America . Palo Alto, CA: Stanford University Press.Google Scholar
McDonald, M. D., and Budge, I.. 2005. Elections, parties, democracy: conferring the median mandate . Oxford: Oxford University Press.CrossRefGoogle Scholar
McDonald, M. D., Mendes, S. M., and Budge, I.. 2004. What are elections for? Conferring the median mandate. British Journal of Political Science 34(1):1–26.CrossRefGoogle Scholar
Merrill, S. III, Grofman, B., and Adams, J.. 2001. Assimilation and contrast effects in voter projections of party locations: evidence from Norway, France, and the USA. European Journal of Political Research 40(2):199–221.CrossRefGoogle Scholar
Miller, W. E., and Stokes, D. E.. 1963. Constituency influence in congress. American Political Science Review 57(1):165–177.CrossRefGoogle Scholar
Monge, G. 1781. Mémoire sur la théorie des déblais et de remblais. Histoire de l’Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année , pp. 666–704.Google Scholar
Myagkov, M., Ordeshook, P. C., and Shakin, D.. 2005. Fraud or fairytales: Russia and ukraine’s electoral experience. Post-Soviet Affairs 21(2):91–131.CrossRefGoogle Scholar
O’Donnell, G. A. 1994. Delegative democracy. Journal of Democracy 5(1):55–69.CrossRefGoogle Scholar
Otero Felipe, P., and Rodríguez Zepeda, J. A.. 2014. Vínculos ideológicos y éxito electoral en América Latina. Política y gobierno 21(1):159–200.Google Scholar
Powell, G. B. Jr. 2000. Elections as instruments of democracy: majoritarian and proportional visions . New Haven: Yale University Press.Google Scholar
Powell, G. B. Jr. 2004. Political representation in comparative politics. Annual Review of Political Science 7(1):273–296.CrossRefGoogle Scholar
Powell, G. B. Jr. 2006. Election laws and representative governments: beyond votes and seats. British Journal of Political Science 36(2):291–315.CrossRefGoogle Scholar
Powell, G. B. Jr. 2009. The ideological congruence controversy: the impact of alternative measures, data, and time periods on the effects of election rules. Comparative Political Studies 42(12):1475–1497.CrossRefGoogle Scholar
Powell, G. B. Jr, and Vanberg, G. S.. 2000. Election laws, disproportionality and median correspondence: implications for two visions of democracy. British Journal of Political Science 30(3):383–411.Google Scholar
Rubner, Y., Tomasi, C., and Guibas, L. J.. 2000. The Earth mover’s distance as a metric for image retrieval. International Journal of Computer Vision 40(2):99–121.CrossRefGoogle Scholar
Saiegh, S. M. 2015. Using joint scaling methods to study ideology and representation: evidence from Latin America. Political Analysis 23(4):363–384.CrossRefGoogle Scholar
Selios, L.2015. Receptividad democrática en América Latina: un análisis de congruencia ideológica en perspectiva diacrónica. Paper presented at VIII Congreso Latinoamericano de Ciencia Política (ALACIP).Google Scholar
Siavelis, P. M. 2009. Elite-mass congruence, partidocracia and the quality of chilean democracy. Journal of Politics in Latin America 1(3):3–31.CrossRefGoogle Scholar
Stokes, S. C. 2001. Mandates and democracy: neoliberalism by surprise in Latin America . Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Urbanek, S., and Rubner, Y.. 2015. Emdist: earth mover’s distance ., R package version 0.3-2.Google Scholar
Wang, F., and Guibas, L. J.. 2012. Supervised earth mover’s distance learning and its computer vision applications. ed. Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., and Schmid, C.. Computer vision—ECCV 2012 , vol. 7572, Berlin: Springer, pp. 442–455.CrossRefGoogle Scholar
Zechmeister, E. 2006. What’s left and who’s right? A q-method study of individual and contextual influences on the meaning of ideological labels. Political Behavior 28(2):151–173.CrossRefGoogle Scholar
Supplementary material: File

Lupu supplementary material

Appendix

Download Lupu supplementary material(File)
File 2 MB