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

Abstract

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.

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Notes

  1. 1.

    For example, in United States elections, African-American voters are very much more likely to vote for the Democratic candidate than they are to vote for the Republican candidate. Thus, it can be said that the Democratic candidate is of higher average valence among African-American voters than the Republican candidate is.

  2. 2.

    We are working on applying the model to the case of Britain, where there are of course at least three regions and regional parties, as well as even greater complexity in Northern Ireland. The first version of the model for Britain (Schofield et al. 2011e) made it clear that it was necessary to develop a regional model.

  3. 3.

    Unable to make a break through in Eastern Canada, the western based Reform Party rebranded itself as the Canadian Reform Alliance Party. Alliance was also unable to appeal to Eastern Canadians. After long deliberations Alliance and the Progressive Conservatives merged in December 2003 to form the Conservative Party of Canada. These types problems in federal systems are not unusual in first-past-the-post plurality systems (Riker 1982).

  4. 4.

    The work described in this paragraph can also be seen in Schofield et al. (2011d) for the UK; in Schofield et al. (2011c) for the US; in Schofield et al. (2011b) for Israel; in Schofield et al. (2011e) for Poland; in Schofield et al. (2011a) Turkey; in Schofield et al. (2012) for Azerbaijan and Georgia; and in Schofield and Zakharov (2010) for Russia.

  5. 5.

    Anocracies are countries in which the president/autocrat governs along an elected legislature. The President, however, exerts undue influence on legislative elections.

  6. 6.

    For example, in Canada, Québec is by the nature of its history, culture and laws different from other provinces; Alberta has vast natural resources (the oil sands); and Ontario has large manufacturing, high tech and service sectors.

  7. 7.

    The Bloc Québécois was created after a failed attempt to bring Québec back into the Canadian Constitution.

  8. 8.

    There may exist parties that may have no national scope but that represent the interest of groups and voters across various provinces or states. Parties with support across various regions may strive to become national players as they grow. Since we examine only one election in the model, we rule out the existence of multi-regional parties as well as the possibility that regional parties can grow to become national parties in the model.

  9. 9.

    In Canada, Albertans care about the oil sands; some Québécers about preserving their French culture and their laws; and Ontarians about policies that affect the manufacturing, high tech and service sectors.

  10. 10.

    We could have assumed instead that the weight of each region depends on the share of seats each region gets in the national parliament. The results presented below would then depend on seat rather than vote shares but would remain substantially unchanged. Note that the number of parliamentary seats that each region gets is, in general, based on the proportion of the population living in that region.

  11. 11.

    If the competence and sociodemographic valences are individual specific, the VCL is able to accommodate parameters of both types by using a random effects hierarchical structure, meaning that the parameters estimated for each region are assumed to come from some probability distribution, generally a normal distribution, as assumed in the SMR model of Sect. 2. This method of estimation is best done utilizing random effects.

  12. 12.

    This is the case for the Bloc Québécois in Canada as the main reason it came into existence was to promote and negotiate the secession of Québec from Canada.

  13. 13.

    Another alternative is the multinomial probit model, which does not rely on the IIA assumption either. However, the multinomial probit model does not allow the researcher to estimate parameters at the level of the individual choice set, i.e., at the regional level, as the errors are absorbed in the error matrix and, thus, the IIA itself is absorbed. However, as with the mixed logit, the regional values are often of as much interest as those at the national level, so the mixed probit is essentially discarding information that the researcher may find useful.

  14. 14.

    In the formal model in Sect. 2, we assume that λ jk and α jk are the mean of the voter’s competence and sociodemographic valences in region k. The assumptions of the formal and empirical models then match, thus making the transition to applying the formal model easier.

  15. 15.

    Canadians were polled almost on a daily basis throughout the campaign with no coverage in the first week or the last three days of the campaign (Pickup and Johnson 2007).

  16. 16.

    The last time a party won more than fifty percent of the vote in Canada was in 1984.

  17. 17.

    As happens in federations where regional differences are accentuated by various political events (Riker 1987).

  18. 18.

    The 5,254 sample reflects the regional, gender and age composition of the Canadian population in the Census (see http://www.ekos.com/admin/articles/26June2004BackgroundDoc.pdf).

  19. 19.

    The factor analysis performed on these questions showed evidence of only two factors or dimensions. Given no evidence of a third factor, the analysis below is carried out using a two dimensional space.

  20. 20.

    While using the mean is a crude measure of party position, other methods, more computationally intensive, provide similar estimates. For example, we used Aldrich and McKelvey (1977) scores to place the parties in the latent policy space. The positions found were not very different from the mean estimates. To check the robustness of estimates from the VCL model with regards to party position we jittered the positions for each party taking 100 random samples from a bivariate normal distribution centered at the mean party positions with a variance of 1 on each axis and no covariance and ran the VCL model. The results show that differences in the estimates only occurred when the draws were far away from the mean positions, meaning that small changes on party positions had little influence the outcome. Given the strong prior information on where parties should be and since these positions match closely with estimates from other papers, we feel confident that using the mean of those voting for the party is a reasonable method for estimating the positions of parties within the created latent policy space.

  21. 21.

    Supporters of the Bloc Québecois are mainly French Québécers who want the cessation of Québec from Canada. Note that not all French Québécers support the Bloc or want greater decentralization. Moreover, according to the 2006 Census, 40 % of the Québec population is none French speaking. Polls suggest that non-French speaking Québécers want Québec to remain in Canada and support greater centralization. It is then not surprising to find that the mean Québécer is neutrally located along the decentralization dimension.

  22. 22.

    This is not uncommon in Federal system with vast regional differences (Riker 1982).

  23. 23.

    The Liberals (LPC), the Conservatives (CPC), the New Democratic Party (NDP) and the Green Party (GPC).

  24. 24.

    As in related work, we assume that the intercept term of the spatial model for each party can be used as an estimate of the party’s competence variance. In our models of US and British politics, we used voter perceptions of candidate traits as estimates of competence valence. However these more refined estimates essentially matched the intercept estimates.

  25. 25.

    Clearly, with 75 out of 308 seats, the BQ leader can never become prime minister in Canada.

  26. 26.

    Note that to avoid having too many rows in Table 4, we included the coefficients by education-age group in the form of a sub-matrix in the corresponding regional regression column.

References

  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.

    Article  Google 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.

    Article  Google 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.

  6. Caplin, A., & Nalebuff, B. (1991). Aggregation and social choice: a mean voter theorem. Econometrica, 59, 1–23.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

  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.

    Article  Google Scholar 

  13. Hotelling, H. (1929). Stability in competition. Economic Journal, 39, 41–57.

    Article  Google 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.

    Google Scholar 

  16. Patty, J. W. (2005). Local equilibrium equivalence in probabilistic voting models. Games and Economic Behavior, 51, 523–536.

    Article  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  20. Poole, K., & Rosenthal, H. (1984). US presidential elections 1968–1980. American Journal of Political Science, 28, 283–312.

    Article  Google Scholar 

  21. Quinn, K., Martin, A., & Whitford, A. (1999). Voter choice in multiparty democracies. American Journal of Political Science, 43, 1231–1247.

    Article  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  25. Riker, W. H. (1987). The development of American federalism. Boston: Kluwer.

    Google 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.

    Article  Google 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.

    Article  Google Scholar 

  30. Schofield, N. (1983). Generic instability of majority rule. Review of Economic Studies, 50, 695–705.

    Article  Google Scholar 

  31. Schofield, N. (2006). Equilibria in the spatial stochastic model of voting with party activists. Review of Economic Design, 10(3), 183–203.

    Article  Google Scholar 

  32. Schofield, N. (2007). The mean voter theorem: necessary and sufficient conditions for convergent equilibrium. Review of Economic Studies, 74, 965–980.

    Article  Google Scholar 

  33. Schofield, N., & Zakharov, A. (2010). A stochastic model of the 2007 Russian Duma election. Public Choice, 142, 177–194.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Google 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.

    Article  Google 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.

    Google 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.

    Article  Google 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:http://ssrn.com/abstract=2309621.

  42. Train, K. (2003). Discrete choice methods for simulation. Cambridge: Cambridge University Press.

    Google Scholar 

  43. Yamamoto, T. (2011). A multinomial response model for varying choice sets, with application to partially contested multiparty elections. Working Paper.

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Acknowledgements

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.

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Correspondence to Norman Schofield.

Empirical Appendix: Election statistics

Empirical Appendix: Election statistics

Table 7 Descriptive statistics of the survey sample by region
Table 8 Descriptive statistics of the survey sample by party and region
Table 9 EKOSa June 21–24, 2004 Poll (Percentages out of 5,254 respondents)b
Table 10 Actual and sample vote shares
Table 11 Provincial votes (%) and seats in the 2004 Canadian election

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Gallego, M., Schofield, N., McAlister, K. et al. The variable choice set logit model applied to the 2004 Canadian election. Public Choice 158, 427–463 (2014). https://doi.org/10.1007/s11127-013-0109-3

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Keywords

  • Stochastic vote model
  • Valence
  • Local Nash equilibrium
  • Convergence coefficient

JEL Classification

  • H10