Public Choice

, Volume 158, Issue 3–4, pp 427–463 | Cite as

The variable choice set logit model applied to the 2004 Canadian election

  • Maria Gallego
  • Norman SchofieldEmail author
  • Kevin McAlister
  • Jee Seon Jeon


Formal work on the electoral model often suggests that parties should locate at the electoral mean. Recent research has found no evidence of such convergence. In order to explain non-convergence, the stochastic electoral model is extended by including a competence and sociodemographic valance in a country where regional and national parties compete in the election. That is, the model allows voters to face different sets of parties in different regions. We introduce the notion of a convergence coefficient, c for regional and national parties and show that when c is high there is a significant centrifugal tendency acting on parties. An electoral survey of the 2004 election in Canada is used to construct a stochastic electoral model of the election with two regions: Québec and the rest of Canada. The survey allows us to estimate voter positions in the policy space. The variable choice set logit model is used to built a relationship between party position and vote share. We find that in the local Nash equilibrium for the election the two main parties with high competence valence, the Liberals and Conservatives, locate at the national electoral mean and the Bloc Québécois, with the highest competence valence, locates at the Québec electoral mean. The New Democratic Party has a low competence valence but remains at the national mean. The Greens, with lowest competence valence, locate away from the national mean to increase its vote share.


Stochastic vote model Valence Local Nash equilibrium Convergence coefficient 

JEL Classification




This paper was presented at the EPSA conference, Barcelona, June 2013; at the political economy panel at the SAET Meeting, Paris, July 2013; the Public Economic Theory (PET) conference in Lisbon, July 2013. We thank seminar participants for their comments. We also thank the two anonymous referees of this paper for their very helpful suggestions.


  1. Adams, J. (2001). Party competition and responsible party government. Ann Arbor: University of Michigan Press. Google Scholar
  2. Adams, J., & Merrill, S. III. (1999). Modeling party strategies and policy representation in multiparty elections: why are strategies so extreme? American Journal of Political Science, 43, 765–781. CrossRefGoogle Scholar
  3. Aldrich, J. H., & McKelvey, R. D. (1977). A method of scaling with applications to the 1968 and 1972 presidential elections. American Political Science Review, 71(1), 111–130. CrossRefGoogle Scholar
  4. Benoit, K., & Laver, M. (2006). Party policy in modern democracies. London: Routledge. Google Scholar
  5. Blais, A., Fournier, P., Gidengil, E., Nevitte, N., & Everitt, J. (2006). Election 2006: how big were the changes…really? Working paper, Universite de Montreal. Google Scholar
  6. Caplin, A., & Nalebuff, B. (1991). Aggregation and social choice: a mean voter theorem. Econometrica, 59, 1–23. CrossRefGoogle Scholar
  7. Clarke, H. D., Kornberg, A., Macleod, J., & Scotto, T. J. (2005). Too close to call: political choice in Canada, 2004. PS, Political Science & Politics, 38, 247–253. CrossRefGoogle Scholar
  8. Dow, J. K., & Endersby, J. (2004). Multinomial logit and multinomial probit: a comparison of choice models for voting research. Electoral Studies, 23, 107–122. CrossRefGoogle Scholar
  9. Downs, A. (1957). An economic theory of democracy. New York: Harper and Row. Google Scholar
  10. Gallego, M., & Schofield, N. (2013). The convergence coefficient across political regimes. Working Paper, Washington University in St. Louis. Google Scholar
  11. Gelman, A., Park, D., Shor, B., Bafumi, J., & Cortina, J. (2008). Red state, blue state, rich state, poor state: why Americans vote the way they do. Princeton: Princeton University Press. Google Scholar
  12. Hinich, M. J. (1977). Equilibrium in spatial voting: the median voter theorem is an artifact. Journal of Economic Theory, 16, 208–219. CrossRefGoogle Scholar
  13. Hotelling, H. (1929). Stability in competition. Economic Journal, 39, 41–57. CrossRefGoogle Scholar
  14. Kramer, G. (1978). Existence of electoral equilibrium. In P. Ordeshook (Ed.), Game theory and political science (pp. 375–389). New York: New York University Press. Google Scholar
  15. Merrill, S., & Grofman, B. (1999). A unified theory of voting. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  16. Patty, J. W. (2005). Local equilibrium equivalence in probabilistic voting models. Games and Economic Behavior, 51, 523–536. CrossRefGoogle Scholar
  17. Patty, J. W. (2006). Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters. Social Choice and Welfare, 28(1), 149–173. Google Scholar
  18. Penn, E. (2009). A model of far-sighted voting. American Journal of Political Science, 53, 36–54. CrossRefGoogle Scholar
  19. Pickup, M., & Johnson, R. (2007). Campaign trial heats as electoral information: evidence from the 2004 and 2006 Canadian federal elections. Electoral Studies, 26, 460–476. CrossRefGoogle Scholar
  20. Poole, K., & Rosenthal, H. (1984). US presidential elections 1968–1980. American Journal of Political Science, 28, 283–312. CrossRefGoogle Scholar
  21. Quinn, K., Martin, A., & Whitford, A. (1999). Voter choice in multiparty democracies. American Journal of Political Science, 43, 1231–1247. CrossRefGoogle Scholar
  22. Riker, W. H. (1964). In Federalism: origin, operation, maintenance. Boston: Little Brown. Google Scholar
  23. Riker, W. H. (1980). Implications from the disequilibrium of majority rule for the study of institutions. American Political Science Review, 74, 432–446. CrossRefGoogle Scholar
  24. Riker, W. H. (1982). The two party system and Duverger’s law: an essay on the history of political science. American Political Science Review, 76, 753–766. CrossRefGoogle Scholar
  25. Riker, W. H. (1987). The development of American federalism. Boston: Kluwer. CrossRefGoogle Scholar
  26. Riker, W. H., & Ordeshook, P. C. (1973). An introduction to positive political theory. Englewood Cliffs: Prentice-Hall. Google Scholar
  27. Roemer, J. E. (2011). A theory of income taxation where politicians focus upon core and swing voters. Social Choice and Welfare, 36, 383–422. CrossRefGoogle Scholar
  28. Saari, D. (1997). The generic existence of a core for q-rules. Economic Theory, 9, 219–260. Google Scholar
  29. Schofield, N. (1978). Instability of simple dynamic games. Review of Economic Studies, 45, 575–594. CrossRefGoogle Scholar
  30. Schofield, N. (1983). Generic instability of majority rule. Review of Economic Studies, 50, 695–705. CrossRefGoogle Scholar
  31. Schofield, N. (2006). Equilibria in the spatial stochastic model of voting with party activists. Review of Economic Design, 10(3), 183–203. CrossRefGoogle Scholar
  32. Schofield, N. (2007). The mean voter theorem: necessary and sufficient conditions for convergent equilibrium. Review of Economic Studies, 74, 965–980. CrossRefGoogle Scholar
  33. Schofield, N., & Zakharov, A. (2010). A stochastic model of the 2007 Russian Duma election. Public Choice, 142, 177–194. CrossRefGoogle Scholar
  34. Schofield, N., Martin, A., Quinn, K., & Whitford, A. (1998). Multiparty electoral competition in the Netherlands and Germany: a model based on multinomial probit. Public Choice, 97, 257–293. CrossRefGoogle Scholar
  35. Schofield, N., Gallego, M., Ozdemir, U., & Zakharov, A. (2011a). Competition for popular support: a valence model of elections in Turkey. Social Choice and Welfare, 36(3–4), 451–480. CrossRefGoogle Scholar
  36. Schofield, N., Claassen, C., Ozdemir, U., & Zakharov, A. (2011b). Estimating the effects of activists in two-party and multiparty systems: a comparison of the United States in 2008 and Israel in 1996. Social Choice and Welfare, 36(3–4), 483–518. CrossRefGoogle Scholar
  37. Schofield, N., Claassen, C., & Ozdemir, U. (2011c). Empirical and formal models of the US presidential elections in 2004 and 2008. In N. Schofield & G. Caballero (Eds.), The political economy of institutions, democracy and voting (pp. 217–258). Berlin: Springer. CrossRefGoogle Scholar
  38. Schofield, N., Gallego, M., & Jeon, J. S. (2011d). Leaders, voters and activists in elections in the Great Britain 2005 and 2010. Electoral Studies, 30(3), 484–496. 2010. CrossRefGoogle Scholar
  39. Schofield, N., Jeon, J. S., Muskhelishvili, M., Ozdemir, U., & Tavits, M. (2011e). Modeling elections in post-communist regimes: voter perceptions, political leaders and activists. In N. Schofield & G. Caballero (Eds.), The political economy of institutions, democracy and voting (pp. 259–301). Berlin: Springer. CrossRefGoogle Scholar
  40. Schofield, N., Jeon, J. S., & Muskhelishvili, M. (2012). Modeling elections in the Caucasus. Journal of Elections, Public Opinion and Parties, 22(2), 187–214. CrossRefGoogle Scholar
  41. Schofield, N., Gallego, M., Jeon, J. S., & Mcalister, K. (2013). The variable choice set logit model applied to the 2004 Canadian election. Working Paper. Available at SSRN:
  42. Train, K. (2003). Discrete choice methods for simulation. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  43. Yamamoto, T. (2011). A multinomial response model for varying choice sets, with application to partially contested multiparty elections. Working Paper. Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Maria Gallego
    • 1
    • 2
  • Norman Schofield
    • 2
    Email author
  • Kevin McAlister
    • 2
  • Jee Seon Jeon
    • 3
  1. 1.Department of EconomicsWilfrid Laurier UniversityWaterlooCanada
  2. 2.Center in Political EconomyWashington UniversitySaint LouisUSA
  3. 3.Department of Political ScienceFlorida State UniversityTallahasseeUSA

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