This book provides a comprehensive mathematical description and analysis of the delegate allocation processes in the US Democratic and Republican presidential primaries, focusing on the role of apportionment methods and the effect of thresholds―the minimum levels of support required to receive delegates. The analysis involves a variety of techniques, including theoretical arguments, simplicial geometry, Monte Carlo simulation, and examination of presidential primary data from 2004 to 2020.
The book is divided into two parts: Part I defines the classical apportionment problem and explains how the implementation and goals of delegate apportionment differ from those of apportionment for state representation in the US House of Representatives and for party representation in legislatures based on proportional representation. The authors then describe how delegates are assigned to states and congressional districts and formally define the delegate apportionment methods used in each state by the two major parties to allocate delegates to presidential candidates.
Part II analyzes and compares the apportionment methods introduced in Part I based on their level of bias and adherence to various notions of proportionality. It explores how often the methods satisfy the quota condition and quantifies their biases in favor or against the strongest and weakest candidates. Because the methods are quota-based, they are susceptible to classical paradoxes like the Alabama and population paradoxes. They also suffer from other paradoxes that are more relevant in the context of delegate apportionment such as the elimination and aggregation paradoxes. The book evaluates the extent to which each method is susceptible to each paradox. Finally, it discusses the appointment of delegates based on divisor methods and notions of regressive proportionality.
This book appeals to scholars and students interested in mathematical economics and political science, with an emphasis on apportionment and social choice theory.
Author(s): Michael A. Jones, David McCune, Jennifer M. Wilson
Series: Studies in Choice and Welfare
Publisher: Springer
Year: 2023
Language: English
Pages: 222
City: Cham
Preface
Acknowledgments
Contents
Abbreviations and Acronyms
Part I Description of Delegate Allocation Rules
1 Apportionment in the US Presidential Primaries
1.1 Apportionment and the Primaries
1.2 What is the Apportionment Problem?
1.3 Apportionment Fundamentals
1.4 Review of the US Primary Process and the History of US Presidential Primaries
1.5 Why Apportionment in Primaries is Different
References
2 The Democratic Party Primary
2.1 Democratic Delegate Plan and Primaries
2.2 Geometry of Hamilton's Method
2.3 Democratic Primaries and Ranked Choice Voting
2.3.1 What Is Ranked Choice Voting?
2.3.2 Ranked Choice Voting and Apportionment
References
3 The Iowa and Nevada Democratic Caucuses
3.1 The 2020 Iowa Caucuses
3.2 The 2020 Nevada Caucuses
References
4 The Republican Party Primary
4.1 Republican Party Delegates
4.2 Thresholds in the Republican Primary
4.3 Republican Selection Rules and Quota-Based Methods
4.3.1 Methods Based on Nearest-Integer Rounding
4.3.2 Methods Based on Lower Quotas
4.3.3 A Method Based on Upper Quotas
4.3.4 Methods that Cannot Be Disentangled from Thresholds
4.3.5 Which States Used Which Methods
4.4 Geometry of Republican Methods
4.5 District Delegates in Republican State Primaries
4.6 Conclusion
References
Part II Analysis of Delegate Allocation Rules
5 Properties of the Apportionment Methods Used in the Primaries
5.1 Properties of the Delegate Apportionment Methods
5.1.1 Proportional Consistency
5.2 Relationship to Quota
5.2.1 Quota Violations in Practice
5.3 Bias
5.3.1 Majorization and Pairwise Comparisons of Bias
5.3.2 Delegate (Seat) Bias
5.3.3 Delegate Thresholds
5.3.4 Extreme Outcomes in Close Elections
5.3.5 Bias in Practice
5.4 Sensitivity to Small Perturbations in Vote Totals
5.4.1 Sensitivity to Vote Totals in Practice
5.5 Majority and Leader Criteria
5.5.1 Majority Criterion
5.5.2 Leader Criterion
5.5.3 Majority and Leader Criteria in Practice
5.6 Support for Candidate Coalitions
5.7 The Cumulative Effect: Comparing Vote Share to Delegate Share
References
6 Paradoxes
6.1 The Elimination Paradox
6.1.1 Geometry of the Elimination Paradox
6.1.2 Likelihood of the Elimination Paradox
6.1.3 Who Is Affected by the Elimination Paradox?
6.1.4 The Effect of Threshold Level on the Elimination Paradox
6.2 The Aggregation Paradox
6.2.1 Geometry of the Aggregation Paradox
6.2.2 Likelihood of the Aggregation Paradox
6.2.3 Who Is Affected by the Aggregation Paradox?
6.2.4 The Effect of Threshold Level on the Aggregation Paradox
6.3 No-Show Paradox
6.3.1 Geometry of the No-Show Paradox
6.3.2 Likelihood of the No-Show Paradox Occurring
6.3.3 Who Is Affected by the No-Show Paradox?
6.3.4 The Effect of Threshold Level on the No-Show Paradox
6.3.5 Weak No-Show Paradox: The Effects of Aggregation
6.4 Alabama Paradox
6.4.1 Geometry of the Alabama Paradox
6.4.2 Likelihood of the Alabama Paradox Occurring
6.4.3 Who Is Affected by the Alabama Paradox?
6.4.4 The Effect of Threshold Level on the Alabama Paradox
6.4.5 The Effect of Aggregation on the Alabama Paradox
6.5 Population Paradox
6.6 Uniformity
6.7 Conclusion
References
7 Exploring Alternative Ways to Allocate Delegates
7.1 Other Apportionment Methods
7.1.1 Shift-Quota Methods
7.1.2 Divisor Methods
7.2 Measures of Fairness
7.3 Degressive Representation in the European Union
7.4 Regressive Representation
7.4.1 Adapting Divisor Methods Using Power Functions
7.4.2 Adapting Divisor Methods Using Weighted Vote Totals
7.5 Conclusion
References
Appendix A Description of the Monte Carlo Simulations
Appendix B Descriptions of the Databases of Primary Election Data
Index
