A Unified Theory of Voting: Directional and Proximity Spatial Models

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Format: Hardcover
Pub. Date: 1999-09-13
Publisher(s): Cambridge University Press
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Summary

This book addresses the questions: how do voters use their own issue positions and those of candidates to decide how to vote? Does a voter tend to choose the candidate who most closely shares the views of the voter or rather a candidate who holds more extreme views due to the fact that the voters discount the candidates' abilities to implement policy. The authors develop a unified model that incorporates these and other voter motivations and assess its empirical predictions - for both voter choice and candidate strategy - in the US, Norway, and France. The analyses show that a combination of proximity, direction, discounting, and party ID are compatible with the mildly but not extremely divergent policies that are characteristic of many two-party and multiparty electorates. All of these motivations are necessary to understand the linkage between candidate issue positions and voter preferences.

Author Biography

Samuel Merrill III is Professor of Mathematics and Computer Science at Wilkes University, Wilkes-Barre, PA. He received a Ph.D. in mathematics from Yale University. His research interests include mathematical modeling in voting behavior, party strategy, and social choice, as well as medical statistics. Bernard Grofman is Professor of Political Science and Social Psychology at the University of California, Irvine. He received a Ph.D. in Political Science from the University of Chicago. His major fields of interest are American politics, comparative election systems, and social choice theory.

Table of Contents

List of Tables and Figures
ix
Acknowledgments xiii
Introduction
1(16)
How Do Voters Decide?
1(3)
Spatial Models
4(6)
Overview
10(7)
PART I Models of Voter Behavior 17(90)
Alternative Models of Issue Voting
19(19)
Proximity Models
19(4)
The Downsian Proximity Model
19(3)
The Grofman Discounting Model
22(1)
Directional Models
23(9)
The Matthews Directional Model
25(4)
The Rabinowitz-Macdonald Directional Model
29(3)
Comparison of Models
32(6)
A Unified Model of Issue Voting: Proximity, Direction, and Intensity
38(14)
Limitations of Pure Models
38(2)
The Unified Model
40(7)
Relation between the Grofman Discounting Model and the RM Model with Proximity Constraint
47(3)
Conclusions
50(2)
Comparing the Empirical Fit of the Directional and Proximity Models for Voter Utility Functions
52(15)
Discriminating between Models
52(1)
Utility Curves
53(6)
Correlation and Regression Analyses of Pure Models of Voter Utility
59(7)
U.S. Data
60(4)
Non-U.S. Data
64(2)
Discussion
66(1)
Empirical Model Fitting Using the Unified Model: Voter Utility
67(14)
Testing the Proximity and Directional Models of Voter Utility within a Nested Statistical Framework
67(1)
Correlation Analysis
68(2)
Fitting the Unified Model of Voter Utility via Nonlinear Regression
70(4)
Parameter Estimates for the Mixed Proximity-RM Model
74(4)
Discussion
78(3)
Empirical Fitting of Probabilistic Models of Voter Choice in Two-Party Electorates
81(10)
Probabilistic Models
81(1)
A Unified Model of Voter Choice
82(2)
Fitting the Conditional Logit Model to American NES Data
84(5)
Discussion
89(2)
Empirical Fitting of Probabilistic Models of Voter Choice in Multiparty Electorates
91(16)
Multiparty Elections
91(1)
Mixed Deterministic and Probabilistic Models
92(3)
Fitting the Conditional Logit Model to Norwegian Data
95(8)
Fitting the Conditional Logit Model to French Data
103(2)
Discussion and Conclusions
105(2)
PART II Models of Party or Candidate Behavior and Strategy 107(57)
Equilibrium Strategies for Two-Candidate Directional Spatial Models
109(19)
Stable Strategies
109(1)
Nash Equilibrium under the Grofman Discounting Model and Constrained Directional Models
110(4)
Nash Equilibria under the Matthews Directional Model
114(9)
Characterization of Condorcet Directional Vectors in Two Dimensions
115(5)
The Condorcet Vacuum for American and Norwegian Data
120(3)
Strategies when Different Models Govern Each Candidate
123(4)
Conclusions
127(1)
Long-term Dynamics of Voter Choice and Party Strategy
128(16)
Why Is There Limited Polarization and Alternation of Parties?
128(3)
Base Dynamic Model under Discounting
131(2)
Convergence to Separate Points of Stability for Each Party under the Base Model
133(2)
Party Strategy under Discounting
135(3)
Modifications of the Model for Asymmetric Parties and Disparate Discount Factors
138(3)
Discussion
141(3)
Strategy and Equilibria in Multicandidate Elections
144(14)
Multicandidate Equilibria
144(1)
A Multidimensional Convergent Equilibrium
145(3)
Divergent Equilibria with Partisan Voting and the Effect of a Directional Component
148(3)
Regions of Candidate Support for Directional Models for More than Two Candidates
151(5)
Discussion and Conclusions
156(2)
Strategy under Alternative Multicandidate Voting Procedures
158(6)
Alternative Voting Procedures
158(2)
Are Centrists or Extremists Favored?
160(1)
Simulation Results
161(1)
Conclusions
162(2)
Postscript Taking Stock of What's Been Done and What Still Needs to Be Done 164(6)
Future Work
166(4)
Appendices 170(25)
3.1 Mixed Proximity-RM Models
170(2)
4.1 Methodology: Data Analysis
172(1)
4.2 Methodology: Linear versus Quadratic Utility Functions
173(1)
4.3Methodology: Mean versus Voter-specific Placements of Candidates
174(5)
5.1 The Nature and Magnitude of Projection Effects
179(2)
5.2 Interpretation of Model Parameters
181(1)
5.3 The Westholm Adjustment for Interpersonal Comparisons
181(5)
7.1 Methodology: The Lewis and King Critique
186(3)
7.2 Methodology: English Translations of Questions from the Norwegian Election Studies
189(1)
7.3 A Strategic Probabilistic Model of Voter Choice
189(2)
8.1 Notes on Equilibrium Analysis
191(2)
8.2 Use of Harmonic Decomposition to Determine Equilibria
193(2)
Glossary of Symbols 195(1)
References 196(11)
Index 207

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