Review of Economic Design

, Volume 10, Issue 3, pp 183–203 | Cite as

Equilibria in the spatial stochastic model of voting with party activists

  • Norman Schofield


Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. Empirical analyses discussed in this paper suggest that convergence of this kind is rarely observed. Here we examine a stochastic electoral model where parties differ in their valences – the electorally perceived, non-policy “quality” of the party leader. It is assumed that valence may either be exogenous, in the sense of being an intrinsic characteristic of the leader, or may be due to the contributions of party activists, who donate time and money and thus enhance electoral support for the party. Theorem 1 shows that vote maximization depends on balancing these two opposed effects. Theorem 2 provides the necessary and sufficient conditions for convergence to the electoral mean when activist valence is zero. The paper then examines empirical electoral models for the Netherlands circa 1980 and Britain in 1979, 1992 and 1997 and shows that party divergence from the electoral mean cannot be accounted for by exogenous valence alone. The balance condition suggests that the success of the Labour party in the election of 1997 can be attributed to a combination of high exogenous valence and pro-Europe activist support.


Local Nash equilibrium Stochastic electoral model Valence Activists 

JEL Classification Numbers

C13 C72 D72 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams J (1999a) Multiparty spatial competition with probabilistic voting. Public Choice 99:259–274CrossRefGoogle Scholar
  2. Adams J (1999b) Policy divergence in multicandidate probabilistic spatial voting. Public Choice 100:103–122CrossRefGoogle Scholar
  3. Adams J (2001) Party competition and responsible party government. University of Michigan Press, Ann ArborGoogle Scholar
  4. Adams J, Merrill III S (1999) Modeling party strategies and policy representation in multiparty elections: why are strategies so extreme?. Am J Polit Sci 43:765–781Google Scholar
  5. Aldrich JH (1983a) A spatial model with party activists: implications for electoral dynamics. Public Choice 41:63–100CrossRefGoogle Scholar
  6. Aldrich JH (1983b) A Downsian spatial model with party activists. Am Polit Sci Rev 77:974–990CrossRefGoogle Scholar
  7. Aldrich JH (1995) Why parties? Chicago University Press, ChicagoGoogle Scholar
  8. Aldrich JH, McGinnis M (1989) A model of party constraints on optimal candidate locations. Math Comput Modell 12(4–5):437–450CrossRefGoogle Scholar
  9. Ansolabehere S, Snyder J (2000) Valence politics and equilibrium in spatial election models. Public Choice 103:327–336CrossRefGoogle Scholar
  10. Aragones E, Palfrey T (2002) Mixed equilibrium in a Downsian model with a favored candidate. J Econ Theory 103:131–161CrossRefGoogle Scholar
  11. Aragones E, Palfrey T (2005) Spatial competition between two candidates of different quality: the effects of candidate ideology and private information. In: Austen-Smith D, Duggan J (eds) Social choice and strategic decisions. Springer, Berlin Heidelberg New YorkGoogle Scholar
  12. Banks J, Duggan J (2000) A bargaining model of collective choice. Am Polit Sci Rev 103:73–88CrossRefGoogle Scholar
  13. Banks J, Duggan J (2005) The theory of probabilistic voting in the spatial model of elections. In: Austen-Smith D, Duggan J (eds) Social choice and strategic decisions. Springer, Berlin Heidelberg New YorkGoogle Scholar
  14. Budge I, Robertson D, Hearl D (eds) (1987) Ideology, strategy and party change: a spatial analysis of post-war election programmes in nineteen democracies. Cambridge University Press, CambridgeGoogle Scholar
  15. Clarke H, Stewart M, Whiteley P (1995) Prime Ministerial approval and governing party support: rival models reconsidered. British J Polit Sci 25(4):597–622Google Scholar
  16. Clarke H, Stewart M, Whiteley P (1997) Tory trends, party identification and the dynamics of Conservative support since 1992. British J Polit Sci 26:299–318CrossRefGoogle Scholar
  17. Clarke H, Stewart M, Whiteley P (1998) New models for new Labour: the political economy of Labour support, January 1992–April 1997. Am Polit Sci Rev 92:559–575CrossRefGoogle Scholar
  18. Clarke H, Sanders MD, Stewart M, Whiteley P (2004) Political choice in Britain. Oxford University Press, OxfordGoogle Scholar
  19. Coughlin P (1992) Probabilistic voting theory. Cambridge Universiry Press, CambridgeGoogle Scholar
  20. Dow J, Endersby J (2004) Multinomial logit and multinomial probit: a comparison of choice models for voting research. Elector Stud 23:07–122Google Scholar
  21. Downs A (1957) An economic theory of democracy. Harper and Row, New YorkGoogle Scholar
  22. Enelow J, Hinich M (1984) The spatial theory of voting: an introduction. Cambridge University Press, CambridgeGoogle Scholar
  23. Giannetti D, Sened I (2004) Party competition and coalition formation: Italy 1994–96. J Theor Polit 16:483–515CrossRefGoogle Scholar
  24. Groseclose T (2001) A model of candidate location when one candidate has a valence advantage. Am J Polit Sci 45:862–886Google Scholar
  25. Hinich M (1977) Equilibrium in spatial voting: the median voter result is an artifact. J Econ Theory 16:208–219CrossRefGoogle Scholar
  26. ISEIUM (1983) European elections study: European political parties’ middle level elites. Europa Institute, MannheimGoogle Scholar
  27. Laver M, Hunt WB (1992) Policy and party competition. Routledge, New YorkGoogle Scholar
  28. Laver M, Schofield N (1990, 1998) Multiparty governments: the politics of coalition in Europe. Oxford University Press, Oxford, (Reprinted) University of Michigan Press, Ann ArborGoogle Scholar
  29. Lin T, Enelow J, Dorussen H (1999) Equilibrium in multicandidate probabilistic spatial voting. Public Choice 98:59–82CrossRefGoogle Scholar
  30. McKelvey RD, Patty J (2006) A theory of voting in large elections. Games Econ Behav (in press)Google Scholar
  31. McKelvey RD, Schofield N (1987) Generalized symmetry conditions at a core point. Econometrica 55:923–933CrossRefGoogle Scholar
  32. Miller G, Schofield N (2003) Activists and partisan realignment in the US. Am Polit Sci Rev 97:245–260CrossRefGoogle Scholar
  33. Quinn K, Martin A (2002) An integrated computational model of multiparty electoral competition. Statist Sci 17:405–419CrossRefGoogle Scholar
  34. Quinn K, Martin A, Whitford A (1999) Voter choice in multiparty democracies. Am J Polit Sci 43:1231–1247Google Scholar
  35. Rabier J, Inglehart R (1981) Eurobarometer II April 1979. The Year of the Child in Europe. Inter-University Consortium for Political and Social Research, Ann ArborGoogle Scholar
  36. Schofield N (1985) Social choice and democracy. Springer, Berlin Heidelberg New YorkGoogle Scholar
  37. Schofield N (2003) Valence competition and the spatial stochastic model. J Theor Polit 15:371–383CrossRefGoogle Scholar
  38. Schofield N (2004) Equilibrium in the spatial valence model of politics. J Theor Polit 16:447–481CrossRefGoogle Scholar
  39. Schofield N (2005) A valence model of political competition in Britain 1992–1997. Elector Stud 24:347–370CrossRefGoogle Scholar
  40. Schofield N (2006) The mean voter theorem: necessary and sufficient conditions for convergent equilibrium. Rev Econ Stud (in press)Google Scholar
  41. Schofield N, Grofman B, Feld S (1989) The core and stability in spatial voting games. Am Polit Sci Rev 82:195–211CrossRefGoogle Scholar
  42. 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 97:257–293CrossRefGoogle Scholar
  43. Schofield N, Miller D, Martin A (2003) Critical elections and political realignments in the US: 1860–2000. Polit Stud 51:217–240CrossRefGoogle Scholar
  44. Schofield N, Sened I (2005a) Modeling the interaction of parties, activists and voters: why is the political center so empty?. Eur J Polit Res 44:355–390CrossRefGoogle Scholar
  45. Schofield N, Sened I (2005b) Multiparty competition in Israel: 1988–1996. British J Polit Sci 36:635–663CrossRefGoogle Scholar
  46. Schofield N, Sened I (2006) Multiparty democracy: elections and legislative politics. Cambridge University Press, CambridgeGoogle Scholar
  47. Sened I (1995) Equilibria in weighted voting games with side-payments. J Theor Polit 7:283–300Google Scholar
  48. Seyd P, Whiteley P (1992) Labour’s grassroots. Clarendon Press, OxfordGoogle Scholar
  49. Seyd P, Whiteley P (2002) New Labour’s Grassroots. Macmillan, Basingstoke, UKGoogle Scholar
  50. Stokes D (1992) Valence politics. In: Kavanagh D (eds) Electoral politics. Clarendon Press, OxfordGoogle Scholar
  51. Train K (2003) Discrete choice methods for simulation. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Center in Political EconomyWashington University in Saint LouisSt LouisUSA

Personalised recommendations