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Social Identity, Electoral Institutions and the Number of Candidates


The empirical literature in comparative politics holds that social cleavages affect the number of candidates or parties when electoral institutions are ‘permissive’, but it lacks a theoretical account of the strategic candidate entry and exit decisions that ultimately determine electoral coalitions in plural societies. This article incorporates citizen-candidate social identities into game-theoretic models of electoral competition under plurality and majority-runoff electoral rules, indicating that social group demographics can affect the equilibrium number of candidates, even in non-permissive systems. Under plurality rule, the relationship between social homogeneity and the effective number of candidates is non-monotonic and, contrary to the prevailing Duvergerian intuition, for some demographic configurations even the effective number of candidates cannot be near two. Empirical patterns in cross-national presidential election results are consistent with the theoretical model.

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1 Duverger Maurice, Political Parties (New York: Wiley, 1954); Ordeshook Peter C. and Shvetsova Olga V., ‘Ethnic Heterogeneity, District Magnitude, and the Number of Parties’, American Journal of Political Science, 38 (1994), 100123; Amorim Neto Octavio and Cox Gary W., ‘Electoral Institutions, Cleavage Structures, and the Number of Parties’, American Journal of Political Science, 41 (1997), 149174; Chhibber Pradeep and Kollman Ken, The Formation of National Party Systems: Federalism and Party Competition in Britain, Canada, India, and the United States (Princeton, N.J.: Princeton University Press, 2004); Roberts Clark William and Golder Matthew, ‘The Sociological and Institutional Determinants of Party Systems Around the World’, Comparative Political Studies, 39 (2006), 679708; Golder Matthew, ‘Presidential Coattails and Legislative Fragmentation’, American Journal of Political Science, 50 (2006), 3448.

2 Lazarsfeld Paul, Berelson Bernard and Gaudet Hazel, The People’s Choice (New York: Columbia University Press, 1944); Campbell Angus, Converse Philip, Miller Warren and Stokes Donald, The American Voter (New York: Wiley, 1960); Martin Lipset Seymour and Rokkan Stein, ‘Cleavage Structure, Party Systems and Voter Alignments’, in Seymour Martin Lipset and Stein Rokkan, eds, Party Systems and Voter Alignments (New York: The Free Press, 1967), pp. 164.

3 See, for example, Bates Robert H., ‘Ethnic Competition and Modernization in Contemporary Africa’, Comparative Political Studies, 6 (1974), 457484; Rabushka Alvin and Shepsle Kenneth, Politics in Plural Societies (Columbus, Ohio: Charles E. Merrill, 1972); Chandra Kanchan, Why Ethnic Parties Succeed (Cambridge: Cambridge University Press, 2004).

4 See, for example, Horowitz Donald, Ethnic Groups in Conflict (Berkeley: University of California Press, 1985).

5 Akerlof George and Kranton Rachel, ‘Economics and Identity’, Quarterly Journal of Economics, 115 (2000), 715753.

6 We therefore take the position that individuals internalize relevant group prescriptions, and that the identity issues in question are therefore psychological in nature rather than a result of external enforcement.

7 Tajfel Henri and Turner John, ‘An Integrative Theory of Intergroup Conflict’, in William G. Austin and Stephen Worchel, eds, The Social Psychology of Intergroup Relations (Monterey, Calif.: Wadsworth, 1979), pp. 3347; Tajfel Henri and Turner John, ‘The Social Identity Theory of Intergroup Behavior’, in Stephen Worchel and William G. Austin, eds, Psychology of Intergroup Relations (Chicago: Nelson-Hall, 1986), pp. 724; Turner John C., ‘Social Identification and Psychological Group Formation’, in Henri Tajfel, ed., The Social Dimension: European Developments in Social Psychology, Vol. 2 (Cambridge: Cambridge University Press, 1984), pp. 518540; Tajfel Henri, Human Groups and Social Categories (Cambridge: Cambridge University Press, 1981).

8 Obviously, the relevant social categories (T) for political competition in the real world are in part endogenous and a matter for contestation. This article takes a given set of politically relevant identities and examines how demographic characteristics and institutional rules interact to determine salient features of the party system.

9 Osborne Martin J. and Slivinski Al, ‘A Model of Political Competition with Citizen-Candidates’, Quarterly Journal of Economics, 111 (1996), 6596; Besley Timothy and Coate Stephen, ‘An Economic Model of Representative Democracy’, Quarterly Journal of Economics, 112 (1997), 85114.

10 This assumption, by which the definitions of salient social groups are exogenous and clearly defined, is nonetheless consistent with the main claim of constructivist scholars of ethnicity. Although social identity categories are clearly constructed, they are often persistent and difficult to reconstruct, particularly over the relatively short time-frames of a single election, as examined here. See, e.g., discussions in Van Evera Stephen, ‘Primordialism Lives!’, Newsletter of the Organized Section in Comparative Politics of the American Political Science Association, 12 (2001), 2022, and Darden Keith, ‘A First Mover Advantage in National Culture: Mass Schooling and the Origins of Nationalism in the USSR’ (Yale University Working Paper, 2004). Obviously, in some contexts, treating social groups as exogenous and clearly defined will not be warranted, but, for many polities, the social groups salient for electoral competition remain stable over substantial periods of time consistent with our assumptions.

11 One possible line of future research is to consider other possible sources of lexicographic preferences over the social identity of political representatives. The assumption of lexicographic preferences drives the key results in the model, and so an alternative account of why voters and candidates have these preferences would provide an alternative mechanism to social identity concerns for the key theoretical and empirical results in this article.

12 Dickson Eric and Scheve Kenneth, ‘Social Identity, Political Speech, and Electoral Competition’, Journal of Theoretical Politics, 18 (2006), 539.

13 Note that kj need not actually be infinite for our results to hold. Instead, what is required for many of our key findings is that kj simply be sufficiently large that identity concerns trump individualistic motivations, so that individual citizens do not act against the group. Precisely how large kj would need to be varies for different propositions in this article; in many cases, it would require additional assumptions about the distribution of policy preferences to characterize the minimum value. This would reduce the generality of the model, and offer a substantial complication without adding much insight, so we simply proceed by assuming kj to be sufficiently large that preferences are effectively lexicographic.

14 Osborne and Slivinski , ‘A Model of Political Competition with Citizen-Candidates’.

15 Osborne and Slivinski , ‘A Model of Political Competition with Citizen-Candidates’.

16 The remainder of the proofs of the propositions are available as Supplementary Materials on the website <>.

17 Duverger , Political Parties.

18 Note that other works suggesting exceptions to the prediction of two-candidate elections under plurality rule have typically arrived at this result in a setting with multiple districts with heterogeneous preferences. See, for example, Morelli Massimo, ‘Party Formation and Policy Outcomes under Different Electoral Systems’, Review of Economic Studies, 71 (2004), 829853, and Callander Steven, ‘Electoral Competition in Heterogeneous Districts’, Journal of Political Economy, 113 (2005), 11161145. Our result identifies a possible set of exceptions in a single district and is a function of divisions within groups in society rather than in differences across districts.

19 Osborne and Slivinski , ‘A Model of Political Competition with Citizen-Candidates’.

20 We are less optimistic about using legislative elections to evaluate the model empirically. Legislative contests under plurality and majority-runoff rules typically take place in multiple geographical districts whose demographic compositions vary from the nation as a whole and from one another but the policy-making function of the legislature depends on coalitions at the national level. Consequently, how entry and exit decisions are determined in these elections is likely to depend on considerations at the district and national level and thus departs substantially from our model.

21 For many values of A, multiple equilibria exist and multiple values of ENPRES are feasible. Because there is no obvious a priori principle for selecting equilibria here, the model cannot in general predict specific values of ENPRES for a specific case. The hypotheses reflect reasonable possibilities for what overall empirical patterns can be expected to look like given the logic of the model and the intuitions contained within Figures 1 and 2.

22 Alesina Alberto, Devleeschauwer Arnaud, Easterly William, Kurlat Sergio and Wacziarg Romain, ‘Fractionalization’, Journal of Economic Growth, 8 (2003), 155194.

23 Golder Matt, ‘Democratic Electoral Systems Around the World, 1946–2000’, Electoral Studies, 24 (2005), 103121.

24 Countries with a fused vote for presidential and legislative elections were not included in the sample.

25 Cox Gary, Making Votes Count (Cambridge: Cambridge University Press, 1997), p. 208.

26 This operationalization assumes that the two largest groups determine the key strategic dynamics in electoral coalition formation. This assumption is of course more plausible: the larger the proportion of citzens that belong to the two largest groups. Below, we discuss ways to incorporate this idea into our empirical analysis. As we discuss in the conclusion, a potentially interesting extension of our theoretical model is to expand the analysis to three or more social groups.

27 Our cross-sectional sample of elections comes from forty-nine countries, twenty-three of which are presidential regimes. The mean (standard deviation) for ENPRES is 3.132 (1.259), for Runoff is 0.714 (0.456), for A is 0.806 (0.156), and for AGT2/3 is 0.796 (0.407). For comparison to previous studies using standard ethnic fractionalization measures, the mean fractionalization score for this sample is 0.410 with a standard deviation of 0.258. The summary statistics for the pooled sample of 101 elections, of which fifty-one are presidential regimes, are extremely similar.

28 Ordeshook and Shvetsova , ‘Ethnic Heterogeneity, District Magnitude, and the Number of Parties’; Neto and Cox , ‘Electoral Institutions, Cleavage Structures, and the Number of Parties’; Clark and Golder , ‘The Sociological and Institutional Determinants of Party Systems Around the World’; Golder , ‘Presidential Coattails and Legislative Fragmentation’.

29 See specifically Golder , ‘Presidential Coattails and Legislative Fragmentation’, p. 43, Equation 2. The important difference is that our measure of social heterogeneity derived from our model is increasing in homogeneity while Golder’s is increasing in heterogeneity. Consequently, the expected signs of the coefficients must be appropriately adjusted.

30 It might be more precise to say that the existing literature’s expectation is that β 2 ⩽ 0. This possibility does not change the contrast with our model discussed below.

31 The exception to this claim is that for the pooled 1990s sample of presidential regimes, there is essentially no difference in variation explained between the specification using A and the specification using the A greater than two-thirds variable.

32 For the same interval, the differences were quite similar for the cross-sectional presidential regime sample (1.20 with a t-statistic of 2.13 for plurality systems and −0.675 with a t-statistic of −1.02 for majority-runoff rule). Varying the interval from [0.62, 0.72] to [0.52, 0.82] yields similar results in that there is a positive difference evident for plurality rule but not for majority runoff.

33 Note that it is not necessary for the analysis to yield similar results across all dimensions of identity for our theory to provide insight, as it may simply be that, on average, ethnicity is the more important social identity for politics. Such a result is consistent with the previous literature’s emphasis on ethnic heterogeneity.

34 Most obviously, any theory that provides a convincing explanation for lexicographic preferences over the social group membership of candidates would generate the same predictions as our model.

* Department of Politics, New York University (email: ), and Department of Political Science, Yale University (email: ), respectively. The authors thank Przemyslaw Nowaczyk and Athanassios Roussias for research assistance, and also Xiaobo Lü, Becky Morton, Athanassios Roussias, Nicholas Sambanis, the Editor of the Journal and its reviewers, as well as seminar participants at UCSD, Princeton University and the University of Michigan for helpful comments.

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British Journal of Political Science
  • ISSN: 0007-1234
  • EISSN: 1469-2112
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