A Unified Theory of Voting

by Samuel Merrill, III , Bernard Grofman

• ISBN13: 9780521665490
• ISBN10: 0521665493
• Format: Paperback
• Copyright: 1999-09-13
• Publisher: Cambridge University Press

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