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The Spatial Model of Politics

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The Spatial Model of Politics Norman Schoeld November 21, 2007 Contents 1 Introduction 1 1.1 Representative Democracy . 1 1.2 The Theory of Social Choice . 8 1.2.1 Restrictions on the Set of Alternatives . 13 1.2.2 Structural Stability of the Core . 18 2 Social Choice 21 2.1 Preference Relations. 21 2.2 Social Preference Functions. 24 2.3 Arrowian Impossibility Theorems . 29 2.4 Power and Rationality . 34 2.5 Choice Functions . 38 3 Voting Rules 45 3.1 Simple Binary Preference Functions . 45 3.2 Acyclic Voting Rules on Restricted Sets of Alternatives . 51 3.3 Manipulation of Choice Functions. 62 3.4 Restrictions on the Preferences of Society . 65 4 The Core 69 4.1 Existence of a Choice. 69 4.2 Existence of the Core in Low Dimension . 73 4.3 Smooth Preference . 79 4.3.1 Non-Convex Preference . 84 4.4 Local Cycles . 87 4.4.1 Necessary and Sufcient Conditions . 89 4.5 Appendix to Chapter 4. 94 5 The Heart 97 5.1 Symmetry Conditions at the Core . 97 5.2 Examples of the Heart and Uncovered Set . .112 iii iv Contents 5.3 Experimental Results . .115 6 A Spatial Model of Coalition 119 6.1 Empirical Analyses of Coalition Formation . .119 6.2 A Spatial Model of Legislative Bargaining . .126 6.3 The Core and the Heart of the Legislature. .132 6.3.1 Examples from Israel . .132 6.3.2 Examples from the Netherlands . .135 6.4 Typologies of Coalition Government . .141 6.4.1 Bipolar Systems . .142 6.4.2 Left Unipolar Systems . .143 6.4.3 Center Unipolar Systems . .147 6.4.4 A Right Unipolar System . .152 6.4.5 Triadic Systems . .153 6.4.6 A Collapsed Core . .155 6.5 Concluding Remarks . .156 6.6 Appendix . .160 7 A Spatial Model of Elections 163 7.1 Political Valence . .163 7.2 Local Nash Equilibrium with Activists . .168 7.3 Empirical Analyses . .179 7.3.1 Elections in Israel. .179 7.3.2 Elections in Turkey 1999-2007 . .183 7.3.3 Elections in the Netherlands . .190 7.3.4 The Election in the United Kingdom in 1997 . .193 7.4 The Inuence of Activists. .195 7.5 Concluding Remarks . .198 7.6 Empirical Appendix . .199 8 Activist Coalitions 203 8.1 Activist Support and Valence. .204 8.2 Argentina's Electoral Dynamics: 1989–1995. .209 8.3 Concluding Remarks . .220 9 Coalitions in the United States 221 9.1 Convergence or Divergence . .221 9.2 Activist Support for the Parties . .224 v 9.2.1 Realignment and Federalism . .229 9.3 Coalitions of Enemies . .232 9.3.1 The New Deal Coalition . .232 9.3.2 The Creation of the Republican Coalition . .233 9.3.3 Social Conservatives Ascendant in the G.O. P.. .236 9.3.4 Stem Cell Research . .238 9.3.5 Immigration . .240 9.4 The Changing Political Equilibrium . .241 9.4.1 Party Dynamics . .244 9.4.2 Party Challenges. .245 9.4.3 Party Switches. .247 9.5 The Future of Republican Populism . .250 9.6 Concluding Remarks . .252 9.7 Appendix: Republican Senator Votes . .257 10 Final Remarks 259 10.1 The Madisonian Scheme of Government . .259 10.2 Preferences and Judgements . .265 vi Contents Tables 6.1 Duration (in months) of government, 1945-1987 120 6.2 Frequency of coalition types, by country, 1945-1987 121 6.3 Duration of European coalitions, 1945-1987 122 6.4 Knesset seats 128 6.5 Seats and votes in the Netherlands 137 6.6 Estimated vote shares and valences in the Netherlands 137 6.7 Seats in the Dutch Parliament, 2003 and 2006 140 6.8 Elections in Denmark, 1957 and 1964 144 6.9 Party and faction strengths in the Dáil Eireann, 1987 150 6.10 Recent elections in Europe 160 7.1 Vote shares and seats in the Knesset 180 7.2 Turkish election results 1999 185 7.3 Turkish election results 2002 185 7.4 Turkish election results 2007 190 7.5 Multinomial Logit Analysis of the 1999 Election in Turkey 199 7.6 Multinomial Logit Analysis of the 2002 Election in Turkey 200 7.7 Log Bayes factors for model comparisons in 1999 201 7.8 Log Bayes factors for model comparisons in 2002 201 9.1 Votes of Republican senators on immigration and stem cell research 257 Figures 3.1 A voting complex 57 4.1 Convex and non-convex preference 85 4.2 Non-convex social preference 87 4.3 Non-convexity of the critical preference cones 89 4.4 Condition for local cyclicity at a point 92 5.1 Euclidean preferences with the q- rule given by (n; q) = (4; 3) 108 5.2 Euclidean preferences with the q- rule given by (n; q) = (6; 4) 109 5.3 Euclidean preferences with the q- rule given by (n; q) = (5; 3) 110 5.4 The heart, the yolk and the uncovered set 113 5.5 The heart with a uniform electorate on the triangle 114 5.6 The heart with a uniform electorate on the pentagon 114 5.7 Experimental results of Fiorina and Plott (1978) 116 5.8 Experimental results of McKelvey and Ordeshook (1978) 116 vii 5.9 Experimental results of Laing and Olmstead (1978) 117 5.10 Experimental results of Laing and Olmstead (1978) 117 5.11 Experimental results of Eavey (1991) 118 5.12 Experimental results of Eavey (1991) 118 6.1 The core in the Knesset in 1992 129 6.2 The heart in the Knesset in 1988 129 6.3 Party positions in the Knesset in 1996 131 6.4 The conguration of the Knesset after the election of 2003 133 6.5 The conguration of the Knesset after the election of 2006 133 6.6 Party positions in the Netherlands in 1977 136 6.7 The Dutch Parliament in 2006 139 6.8 Finland in 2003 142 6.9 Denmark in 2001 145 6.10 Sweden in 2002 145 6.11 Norway in 2001 146 6.12 The heart in Belgium in 1999 148 6.13 The heart in Belgium in 2003 149 6.14 Ireland in 1987 151 6.15 Ireland in 2007 152 6.16 Iceland in 2003 153 6.17 Austria in 2006 154 6.18 Germany in 2002 155 6.19 The core in Italy in 1987 156 6.20 Italy in 2001 157 7.1 The Gumbel distribution 170 7.2 A local Nash equilibrium in the Knesset in 1996 182 7.3 Party positions and voter distribution in Turkey in 1999 186 7.4 The heart in Turkey in 1999 186 7.5 Party positions and voter distribution in Turkey in 2002 187 7.6 Party positions in the Netherlands 192 7.7 Party positions in the United Kingdom 194 7.8 Balance loci for parties in Britain 194 8.1 Activists in Argentina 213 8.2 The voter distribution in Argentina in 1989 219 9.1 Activists in the United States 225 10.1 Estimated positions of posssible candidates for the U.S. presidency 271 Foreword The last half century has witnessed the conuence of several intellec- tual tributaries in formal political theory. The earliest of these, dating from the second decade of the twentieth century and crowned by a mag- num opus in 1944, was cooperative game theory. Von Neumann and Morgenstern's The Theory of Games and Economic Behavior (Prince- ton, 1944) is arguably the most signicant single achievement in social science theory in the last century. And Luce and Raiffa's Games and De- cisions (Wiley, 1957) served as a seminal textbook, popularizing many of the tools developed there. Commencing not too long after was social choice theory, which may be dated with the appearance of Kenneth Ar- row's Social Choice and Individual Values (Wiley, 1951), though it was preceded in the 1940s by several of his own papers as well as those by Duncan Black (and several centuries earlier by the work of Condorcet and Borda). Spatial models, the third tributary, also is associated with work early in the twentieth century, principally that of Harold Hotelling. But its real relevance for political science emerged in the 1950s with An- thony Downs's An Economic Theory of Democracy (Harper and Row, 1957) and Duncan Black's Theory of Committees and Elections (Cam- bridge, 1958). A fourth tributary is non-cooperative game theory, devel- oped as an offshoot of the earlier work by von Neumann and Morgen- stern in seminal papers by John Nash, but reached its zenith in the late 1970s as it took over eld after eld in economics (for overviews, see especially James Friedman, Oligopoly and the Theory of Games (North- Holland, 1977), Drew Fudenberg and Jean Tirole, Game Theory (MIT, 1991), and David Kreps, A Course in Microeconomic Theory (Princeton, 1990)). A fth tributary, another offshoot of cooperative game theory, was coalition theory, developed most prominently in political science by William Riker, The Theory of Political Coalitions (Yale, 1962). Need- less to say, there were second-order intellectual descendants, but these are the principal branches. For quite some time each of these lived an independent existence, ix x Foreword their fruits harvested by separate communities of scholars with only the occasional cross-over (as in William Riker and Peter Ordeshook, An In- troduction to Positive Political Theory (Prentice-Hall, 1972)). One of the leading innovators, drawing from (and making important contribu- tions to) all of these traditions, is Norman Schoeld. The present volume is something of a grand synthesis.
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