Skip to main content
×
×
Home

Was Duverger Correct? Single-Member District Election Outcomes in Fifty-three Countries

  • Matthew M. Singer
Abstract

In districts where only one seat is contested, the electoral formula (plurality or majority) should be a major determinant of the number of parties that receive votes. Specifically, plurality rule should generate two-party competition while other institutional arrangements should generate electoral fragmentation. Yet tests of these propositions using district-level data have focused on a limited number of cases; they rarely contrast different electoral systems and have reached mixed conclusions. This study analyses district-level data from 6,745 single-member district election contests from 53 democratic countries to test the evidence for Duverger's Law and Hypothesis. Double-ballot majoritarian systems have large numbers of candidates, as predicted, but while the average outcome under plurality rule is generally consistent with two-party competition, it is not perfectly so. The two largest parties typically dominate the districts (generally receiving more than 90 per cent of the vote), and there is very little support for parties finishing fourth or worse. Yet third-place parties do not completely disappear, and ethnic divisions shape party fragmentation levels, even under plurality rule. Finally, institutional rules that generate multiparty systems elsewhere in the country increase electoral fragmentation in single-member plurality districts.

Copyright
Footnotes
Hide All
*

Department of Political Science, University of Connecticut (email: matthew.m.singer@uconn.edu). The author thanks Ethan Scheiner, Rob Moser and Laura Stephenson for comments on previous drafts and claims responsibility for all errors. An online appendix is available at http://dx.doi.org/10.1017/S0007123412000233. Supplementary materials are available at the author's website http://www.polisci.uconn.edu/people/faculty/faculty.php?name=singer. Replication data are available via email.

Footnotes
References
Hide All

1 Duverger, Maurice, Political Parties (London: Methuen Press, 1954), p. 217

2 Duverger, Political Parties, p. 239

3 Riker, William H., ‘The Two-Party System and Duverger's Law: An Essay on the History of Political Science’, American Political Science Review, 76 (1982), 753766

4 Gallagher, Michael and Mitchell, Paul, eds, The Politics of Electoral Systems (New York: Oxford University Press, 2005), pp. 2556

Taagepera, Rein, Predicting Party Sizes: The Logic of Simple Electoral Systems (Oxford: Oxford University Press, 2007)

5 Gaines, Brian J., ‘Duverger's Law and the Meaning of Canadian Exceptionalism’, Comparative Political Studies, 32 (1999), 835861

Grofman, Bernard, Blais, André and Bowler, Shaun, eds, Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States (New York: Springer, 2009), pp. 115134

Chhibber, Pradeep and Kollman, Ken, The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India, and the United States (Princeton, NJ: Princeton University Press, 2004)

Grofman, Blais and Bowler, Duverger's Law of Plurality Voting, pp. 83–96

6 Grofman, Bernard, Blais, André and Bowler, Shaun, Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States (New York: Springer, 2009), p. 2

7 Cox, Gary W., Making Votes Count: Strategic Coordination in the World's Electoral Systems (Cambridge: Cambridge University Press, 1997)

8 Singer, Matthew M. and Stephenson, Laura J., ‘The Political Context and Duverger's Theory: Evidence at the District Level’, Electoral Studies, 28 (2009), 480491

9 Reilly, Benjamin, ‘Party Politics in Papua New Guinea: A Deviant Case?’ Pacific Affairs, 72 (1999), 225246

Diwakar, Rekha, ‘Duverger's Law and the Size of the Indian Party System’, Party Politics, 13 (2007), 539561

Grynaviski, Jeffrey D., ‘The Impact of Electoral Rules on Factional Competition in the Democratic South, 1919-48’, Party Politics, 10 (2004), 499519

10 Chhibber and Kollman, The Formation of National Party Systems; Grofman, Blais and Bowler, Duverger's Law of Plurality Voting.

11 Moser, Robert G., Unexpected Outcomes: Electoral Systems, Political Parties, and Representation in Russia (Pittsburgh: University of Pittsburgh Press, 2001)

Moser, Robert G. and Scheiner, Ethan, ‘Mixed Electoral Systems and Electoral System Effects: Controlled Comparison and Cross-National Analysis’, Electoral Studies, 23 (2004), 575599

Reed, Steven R., ‘Duverger's Law is Working in Italy’, Comparative Political Studies, 34 (2001), 312327

Nishikawa, Misa and Herron, Erik S., ‘Mixed Electoral Rules’ Impact on Party Systems’, Electoral Studies, 23 (2004), 753768

Cox, Karen E. and Schoppa, Leonard J., ‘Interaction Effects in Mixed-Member Electoral Systems: Theory and Evidence From Germany, Japan, and Italy’, Comparative Political Studies, 35 (2002), 10271053

12 Singer and Stephenson, ‘The Political Context and Duverger's Theory’ shows that changes in district magnitude affect the number of parties that receive votes in 58 democratic countries. While in that study we explore variations in district magnitude and hold the electoral formula relatively constant, here I hold the district magnitude constant and focus on the effect of changes in electoral formula.

13 Clark, William and Golder, Matt, ‘Rehabilitating Duverger's Theory: Testing the Mechanical and Strategic Modifying Effects of Electoral Laws’, Comparative Political Studies, 39 (2006), 679708

Benoit, Kenneth, ‘District Magnitude, Electoral Formula, and the Number of Parties’, European Journal of Political Research, 39 (2001), 203229

14 Black, Jerome H., ‘The Multicandidate Calculus of Voting: Application to Canadian Federal Elections’, American Journal of Political Science, 22 (1978), 609638

Evans, Geoffrey and Heath, Anthony, ‘A Tactical Error in the Analysis of Tactical Voting’, British Journal of Political Science, 23 (1993), 131137

Alvarez, Michael and Nagler, Jonathan, ‘A New Approach for Modelling Strategic Voting in Multiparty Elections’, British Journal of Political Science, 30 (2000), 5775

Abramson, Paul R., Aldrich, John H., Diamond, Matthew, Diskin, Abraham, Levine, Renan and Scotto, Thomas J., ‘Strategic Abandonment or Sincerely Second Best? The 1999 Israeli Prime Ministerial Election’, Journal of Politics, 66 (2004), 706728

Merolla, Jennifer and Stephenson, Laura B., ‘Strategic Voting in Canada: A Cross Time Analysis’, Electoral Studies, 26 (2007), 235246

Bowler, Shaun and Lanoue, David J., ‘Strategic and protest Voting for Third Parties: The Case of the Canadian NDP’, Political Research Quarterly, 45 (1992), 485499

Blais, André and Turgeon, Mathieu, ‘How Good are Voters at Sorting Out the Weakest Candidate in their Constituency?’, Electoral Studies, 23 (2004), 455461

15 Aldrich, John, Why Parties? The Origin and Transformation of Political Parties in the United States (Chicago: University of Chicago Press, 1995)

Blais, André and Carty, R.K., ‘The Psychological Impact of Electoral Laws: Measuring Duverger's Elusive Factor’, British Journal of Political Science, 21 (1991), 7993

16 Clark and Golder, ‘Rehabilitating Duverger's Theory’; Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

17 Dickson, Eric and Scheve, Ken, ‘Social Identity, Electoral Institutions, and the Number of Candidates’, British Journal of Political Science, 40 (2010), 349375

18 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

19 Blais, André and Indridason, Indridi, ‘Making Candidates Count: The Logic of Electoral Alliances in Two-Round Legislative Elections’, Journal of Politics, 69 (2007), 193205

III, Charles S. Bullock and Johnson, Loch K., Runoff Elections in the United States (Chapel Hill: University of North Carolina Press, 1992)

Spoon, Jae-Jae, ‘Evolution of New Parties: From Electoral Outsiders to Downsian Players – Evidence from the French Greens’, French Politics, 5 (2007), 121124

20 Duverger, Political Parties, p. 228

21 Grofman, Bernard, Lee, Sung-Chull, Winckler, Edwin and Woodall, Brian, Elections in Japan, Korea and Taiwan under the Single Non-Transferable Vote: The Comparative Study of an Embedded Institution (Ann Arbor: University of Michigan Press, 1999)

22 Shugart, Matthew S. and Wattenberg, Martin, Mixed-Member Electoral Systems: The Best of Both Worlds? (Oxford: Oxford University Press, 2001)

Scheiner, Ethan, ‘Does Electoral System Reform Work? Electoral System Lessons from Reforms of the 1990s’, Annual Review of Political Science, 11 (2008), 161181

23 Herron, Erik S. and Nishikawa, Misa, ‘Contamination Effects and the Number of Parties in Mixed-Superposition Electoral Systems’, Electoral Studies, 20 (2001), 6386

24 Monroe, Burt L. and Rose, Amanda G., ‘Electoral Systems and Unimagined Consequences: Partisan Effects of Districted Proportional Representation’, American Journal of Political Science, 46 (2002), 6789

25 Samuels, David J. and Shugart, Matthew S., ‘Presidentialism, Elections and Representation’, Journal of Theoretical Politics, 15 (2003), 3360

26 Shugart, Matthew S. and Carey, John, Presidents and Assemblies (New York: Cambridge University Press, 1992)

27 Lago, Ignacio and Montero, Jose, ‘Coordination Between Electoral Arenas in Multilevel Countries’, European Journal of Political Research, 48 (2009), 176203

28 Cox, Gary W., ‘Electoral Rules and Electoral Coordination’, Annual Review of Political Science, 2 (1999), 145161

29 Brancati, Dawn, Peace by Design: Managing Ethnic Conflict through Decentralization (Oxford: Oxford University Press, 2009)

30 E.g., Johnston and Cutler, ‘Canada: The Puzzle of Local Three-Party Competition’.

31 Diwaker, Rekha, ‘Duverger's Law and the Size of the Indian Party System’, Party Politics, 13 (2007), 539561

32 Chhibber and Kollman, The Formation of National Party Systems; Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

33 Dickson and Scheve, ‘Social Identity, Electoral Institutions, and the Number of Candidates’.

34 Neto, Octavio Amorim and Cox, Gary W., ‘Electoral Institutions, Cleavage Structures, and the Number of Parties’, American Journal of Political Science, 41 (1997), 149174

35 Reynolds, Andrew, ed., The Architecture of Democracy: Institutional Design, Conflict Management, and Democracy in the Late Twentieth Century (New York: Cambridge University Press, 2002), pp. 248265

Duch, Raymond M., ‘A Developmental Model of Heterogeneous Economic Voting in New Democracies’, American Political Science Review, 98 (2001), 895910

36 Moser, Unexpected Outcomes.

37 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

38 Moser and Scheiner, ‘Mixed Electoral Systems and Electoral System Effects’.

39 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

40 Gaines, ‘Duverger's Law and the Meaning of Canadian Exceptionalism’; Gaines, ‘Does the United Kingdom Obey Duverger's Law?’, Johnson and Cutler, ‘Canada: The Puzzle of Local Three-Party Competition’; and Diwaker, ‘Duverger's Law and the Size of the Indian Party System’.

41 Chhibber, Pradeep and Kollman, Ken, ‘Party Aggregation and the Number of Parties in India and the United States’, The American Political Science Review, 92 (1998), 329342

42 Chhibber, Pradeep and Kollman, Ken, ‘Party Aggregation and the Number of Parties in India and the United States’, p. 53

43 Grofman, Blais and Bowler, Duverger's Law of Plurality Voting. It is worth noting that most of the chapters in this book do not analyse district-level outcomes but instead look at the number of parties nationally or strategic-voting patterns, thus testing Duverger's underlying mechanism but not his basic prediction.

44 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

45 Reed, ‘Duverger's Law is Working in Italy’.

46 Moser and Scheiner, ‘Mixed Electoral Systems and Electoral System Effects’.

47 Cox and Schoppa, ‘Interaction Effects in Mixed-Member Electoral Systems’.

48 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

49 Jones, Mark P., ‘Racial Heterogeneity and the Effective Number of Candidates in Majority Runoff Elections: Evidence From Louisiana’, Electoral Studies, 16 (1997), 349358

50 Jones, Mark P., ‘Electoral Laws and the Effective Number of Candidates in Presidential Elections’, Journal of Politics, 61 (1999), 171184

Golder, Matt, ‘Presidential Coattails and Legislative Fragmentation’, American Journal of Political Science, 50 (2006), 3448

51 Cox, Making Votes Count.

52 Laakso, Marku and Taagepera, Rein, ‘The “Effective” Number of Parties: A Measure with Application to West Europe’, Comparative Political Studies, 12 (1979), 327

Taagepera, Rein, ‘Effective Number of Parties for Incomplete Data’, Electoral Studies, 16 (1997), 145151

53 Grofman, Blais and Bowler, Duverger's Law of Plurality Voting.

54 Taagepera, Predicting Party Sizes, p. 103

55 Chhibber and Kollman, The Formation of National Party Systems.

56 For example, a distribution of votes across three parties in which the winner receives 39 per cent of the vote, the second-place party 38 per cent and the third-place party 13 per cent yields an effective number of parties of 2.5. A district where the top three parties receive 57, 23 and 20 per cent of the vote, respectively, also qualifies as a two-party competition under this standard. Yet both of these scenarios imply that there is a substantial third candidate in the district (even if in the second case, strategic coordination by the two losing parties could not have changed the outcome).

57 While the empirical tests focus on the support for parties finishing third or worse, I supplement the discussion by looking at the distribution of votes for parties finishing first and second as well. This approach follows the advice of Taagepera, Predicting Party Sizes, p. 106 to differentiate whether FPTP yields distributions of the vote of ‘52-48 or 50-40-10’. I do not have a specific hypothesis about support for first- and second-place parties because Duverger's Law does not have any implications for cases in which there is only demand for one party in a district (Clark and Golder, ‘Rehabilitating Duverger's Theory’). In other words, Duverger's Law can be satisfied when support for the second-place party ranges from 0–50 per cent as long as the winning party gets the rest of the votes in the district.

58 Gaines, ‘Duverger's Law and the Meaning of Canadian Exceptionalism’. The distributions of these various dependent variables are graphed in the online appendix.

59 Cox, Making Votes Count.

60 Cox, Making Votes Count considers cases with an SF ratio of 1 to be potential exemplars of a non-Duvergerian equilibrium, in which voters do not know which party is in third place and thus should be abandoned. However, the key point for this analysis is that such a scenario does not correspond to a two-party competition.

61 Several contributors to Grofman, Blais and Bowler, Duverger's Law of Plurality Voting argue that another indicator of strategic coordination failure by voters and elites is if support for third place or worse parties is greater than the margin between the first- and second-place parties. In districts where small parties gained more support than the victor's margins, strategic coordination by all small party supporters could potentially have changed the race's outcome. This is equivalent to modelling whether the winning party received 50 percent of the vote or not. This kind of outcome should be relatively rare under the strategic outcome Duverger envisions. I have thus also analysed this question and present the results in the online appendix.

62 The 2010 British election was more fragmented than was the 1997 election used in this dataset, but the substantive conclusions do not change if we use the 2010 elections instead (see the online appendix).

63 I exclude Papua New Guinea from the analysis because it is such a large outlier from the dominant pattern in other countries using the same system, even after controlling for other factors (Reilly, ‘Party Politics in Papua New Guinea’; Singer and Stephenson, ‘The Political Context and Duverger's Theory’).

64 Mylonas, Harris and Roussias, Nasos, ‘When Do Votes Count? Regime Type, Electoral Conduct, and Political Competition in Africa’, Comparative Political Studies, 41 (2008), 14661491

65 Caramani, Daniele, Elections in Western Europe since 1815: Electoral Results by Constituencies (New York: MacMillan, 2000)

66 I have also run the analysis excluding these three countries, and the substantive results do not change. All variables that are significant at conventional levels when they are included are significant when they are excluded.

67 Shugart and Carey, Presidents and Assemblies. I have run models with controls for the president's electoral system in non-concurrent elections and find no effect.

68 Beck, Thorsten, Clarke, George, Groff, Alberto, Keefer, Philip and Walsh, Patrick, ‘New Tools in Comparative Political Economy: The Database of Political Institutions’, World Bank Economic Review, 15 (2001), 165176

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

70 Stoll, Heather, ‘Social Cleavages and the Number of Parties: How the Measures You Choose Affect the Answers You Get’, Comparative Political Studies, 41 (2008), 14391465

71 Neto, Amorim and Cox, ‘Electoral Institutions, Cleavage Structures, and the Number of Parties’, p. 168

Jones, ‘Racial Heterogeneity and the Effective Number of Candidates in Majority Runoff Elections’, pp. 350–351

Singer and Stephenson, ‘The Political Context and Duverger's Theory’, p. 484

72 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

73 Moser, Unexpected Outcomes; Moser and Scheiner, ‘Mixed Electoral Systems and Electoral System Effects’.

74 Grofman, Blais and Bowler, Duverger's Law of Plurality Voting, p. 10

75 Steenbergen, Marco R. and Jones, Bradford S., ‘Modeling Multilevel Data Structures’, American Journal of Political Science, 46 (2002), 218237

Anderson, Christopher J. and Singer, Matthew M., ‘The Sensitive Left and the Impervious Right: Multilevel Models and the Politics of Inequality, Ideology, and Legitimacy in Europe’, Comparative Political Studies, 44 (2008), 564599

Maas, Cora and Hox, Joop, ‘Robustness Issues in Multilevel Regression Analysis’, Statisca Neerlandica, 58 (2002), 127137

76 Since none of the countries in this sample combine plurality electoral rules with majoritarian presidential rules, there is no control for majoritarian presidential elections in this model.

77 E.g., Gaines, ‘Duverger's Law and the Meaning of Canadian Exceptionalism’; Diwaker, ‘Duverger's Law and the Size of the Indian Party System’; Grofman, Blais and Bowler, Duverger's Law of Plurality Voting.

78 Moreover, the model provides no evidence in the initial specification that size or federalism raises fragmentation generally in FPTP countries, so we cannot attribute the different outcomes in Canada, India or the UK to these characteristics.

79 Grofman, Blais and Bowler, Duverger's Law of Plurality Voting uses the standard of whether votes for parties outside the top two parties were greater than the margin of victory to identify districts in which strategic voting potentially could have swung the election (which is equivalent to asking if the winner got a majority of the vote) and thus to diagnose coordination failures. However, this only defines an upper limit on the number of cases in which strategic behaviour could change the outcome. In some of these cases, small party voters may have been indifferent between the top two or preferred the winner, meaning that strategic behaviour would have left the outcome unchanged.

80 The third-place party was only bigger than the margin between the top two parties in 1.4 per cent of American districts, but could have swung the election in 30 per cent of the districts in Canada, 36 per cent of the districts in the UK, 43 per cent of the districts in India or Zambia, and 75 per cent of the districts in Nepal.

81 Clark and Golder, ‘Rehabilitating Duverger's Theory’.

82 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

83 The TF coefficient is significant at 0.05 in the results presented in online appendix 9; it is significant at the 0.10 level here.

84 Monroe and Rose, ‘Electoral Systems and Unimagined Consequences’; Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

85 See online appendix 9.

86 Moser, Unexpected Outcomes; Moser and Scheiner, ‘Mixed Electoral Systems and Electoral System Effects’.

87 Reed, ‘Duverger's Law is Working in Italy’.

88 Chhibber and Kollman, The Formation of National Party Systems; Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

89 Singer and Stephenson, ‘The Political Context and Duverger's Theory’.

90 Monroe and Rose, ‘Electoral Systems and Unimagined Consequences’.

91 Chhibber and Kollman, The Formation of National Party Systems.

92 A cross-sectional correlation between the number of parties winning votes/seats nationally versus locally may reflect a feedback loop, or may be the result of extrapolating district-level electoral fragmentation onto the national level.

93 Support for the first, second, third and remaining parties averages 46-30-11-12 in MMP districts, 46-30-12-11 in PR districts and 49-30-13-7 in Canada, India and the UK.

94 The top two parties receive 90 per cent or more of the vote 72 per cent of the time in plurality elections outside of Canada, India and the UK, compared to 32 per cent of the time in mixed systems, 18 per cent of the time in Canada, India and the UK, and less than 1 per cent of districts under majority rule.

* Department of Political Science, University of Connecticut (email: ). The author thanks Ethan Scheiner, Rob Moser and Laura Stephenson for comments on previous drafts and claims responsibility for all errors. An online appendix is available at http://dx.doi.org/10.1017/S0007123412000233. Supplementary materials are available at the author's website http://www.polisci.uconn.edu/people/faculty/faculty.php?name=singer. Replication data are available via email.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

British Journal of Political Science
  • ISSN: 0007-1234
  • EISSN: 1469-2112
  • URL: /core/journals/british-journal-of-political-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
Type Description Title
WORD
Supplementary materials

Singer Supplementary Material
Appendix

 Word (74 KB)
74 KB

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed