Analysing multiparty competition in plurality rule elections

The study of general election outcomes can be helped by finding better approaches for visualizing large quantities of information and asking questions about its patterning. We review the Nagayama or ‘all possibilities' triangle display, and show that it can only legitimately be used to show an overall ‘field’ of results that is logically feasible, called the effective space of competition, which varies with the number of observable parties. We apply this reductionist view to analysing outcomes in three leading plurality rule systems (the USA, India and Great Britain), focusing on evidence of the Duvergerian psychological effect acting on voters during campaign periods. The Effective Competition Space view illuminates some key differences across countries, and variations with rising numbers of parties competing. We next consider a more holistic approach, the ‘crown’ diagram, which links electoral district outcomes more closely to the most important politico-ideological dimension in each country. Both views suggest some tentative evolutionary hypotheses for the variegated development of plurality rule systems over time. Britain is a highly nationalized party system, but one that has moved substantially away from Duvergerian predictions of two-party focusing, and towards multiparty politics. The USA seems to be a case of ‘stunted development’. India shows a partial Duvergerian conformity, yet combined with a substantial vertical scatter of non-Duvergerian results. Applications to over-time and regional analysis within countries are also sketched.

[1]  Kenneth F. Scheve,et al.  Social Identity, Electoral Institutions and the Number of Candidates , 2010, British Journal of Political Science.

[2]  Patrick Dunleavy.  New Worlds in Political Science , 2010 .

[3]  R. Diwakar.  Duverger's Law and the Size of the Indian Party System , 2007 .

[4]  Jeffrey D. Grynaviski.  The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India, and the United , 2007, The Journal of Politics.

[5]  Guojun Gan,et al.  Data Clustering: Theory, Algorithms, and Applications (ASA-SIAM Series on Statistics and Applied Probability) , 2007 .

[6]  A. Fielding.  Cluster and Classification Techniques for the Biosciences: Preface , 2006 .

[7]  Pradeep K. Chhibber,et al.  Duvergerian Dynamics in the Indian States , 2006 .

[8]  Anna Likhtenchtein,et al.  Duverger's equilibrium under limited competition: Russia's parliamentary elections , 2005 .

[9]  Patrick Dunleavy,et al.  The Impact of UK Electoral Systems , 2005 .

[10]  Mathew Sobert Shugart.  Comparative Electoral Systems Research: The Maturation of a Field and New Challenges Ahead , 2005 .

[11]  Patrick Dunleavy.  Facing Up to Multi-Party Politics: How Partisan Dealignment and PR Voting Have Fundamentally Changed Britain’s Party Systems , 2005 .

[12]  L. Erickson.  The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India and the United States , 2005, Perspectives on Politics.

[13]  A. Sikk,et al.  How unstable? Volatility and the genuinely new parties in Eastern Europe , 2005 .

[14]  É. Bélanger.  Antipartyism and Third-Party Vote Choice , 2004 .

[15]  Rein Taagepera,et al.  Extension of the Nagayama Triangle for Visualization of Party Strengths , 2004 .

[16]  Patrick Dunleavy,et al.  Constructing the Number of Parties , 2003 .

[17]  S. Reed.  What Mechanism Causes the M + 1 Rule? A Simple Simulation , 2003, Japanese Journal of Political Science.

[18]  M. Laver,et al.  The Evolution of Party Systems between Elections , 2003 .

[19]  Steven R. Reed,et al.  Duverger's Law is Working in Italy , 2001 .

[20]  D. Saari.  Explaining All Three-Alternative Voting Outcomes , 1999 .

[21]  Ken Kollman,et al.  Party Aggregation and the Number of Parties in India and the United States , 1998, American Political Science Review.

[22]  M. L. Mitchell,et al.  Visual Explanations: Images and Quantities, Evidence and Narrative , 1997 .

[23]  G. Cox.  Making Votes Count: Strategic Coordination in the World's Electoral Systems , 1997 .

[24]  E. Tufte.  Visual explanations: images and quantities, evidence and narrative , 1997 .

[25]  S. Hug.  The emergence of new political parties from a game theoretic perspective , 1996 .

[26]  Stuart Macdonald,et al.  New Players in an Old Game , 1991 .

[27]  S. Reed.  Structure and Behaviour: Extending Duverger's Law to the Japanese Case , 1990, British Journal of Political Science.

[28]  Michael C. Munger,et al.  Seats and Votes: The Effects and Determinants of Electoral Systems , 1990, American Political Science Review.

[29]  W. Irvine.  Seats and Votes: The Effects and Determinants of Electoral Systems Rein Taagepera and Matthew Soberg Shugart New Haven: Yale University Press, 1989, pp. xviii, 292 , 1989, Canadian Journal of Political Science.

[30]  N. Schofield.  The Geometry of Voting , 1983 .

[31]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[32]  M. Duverger.  Political Parties Their Organization and Activity in the Modern State , 1964 .

[33]  T. Kuhn,et al.  The Structure of Scientific Revolutions , 1963 .

[34]  R. Taagepera.  Predicting party sizes: the logic of simple electoral systems , 2007 .

[35]  R. Diwakar.  An investigation into the determinants of the size of Indian party systems , 2006 .

[36]  M. Laver,et al.  The Integer Arithmetic of Legislative Dynamics , 2005 .

[37]  P. Norris,et al.  Britain votes 2005 , 2005 .

[38]  S. Hug.  Altering Party Systems: Strategic Behavior and the Emergence of New Political Parties in Western Democracies , 2001 .

[39]  Donald G. Saari,et al.  Chaotic Elections! - A Mathematician Looks at Voting , 2001 .

[40]  D. Saari.  Basic Geometry of Voting , 1995 .

[41]  B. Szajkowski.  Political Parties of Eastern Europe, Russia and the successor states , 1994 .

[42]  E. Tufte.  Envisioning Information , 1990 .

[43]  T. Kuhn.  The Structure of Scientific Revolutions. Chicago (University of Chicago Press) 1962. , 1962 .