This introductory textbook on social choice theory makes the social choice theoretic framework and its main results, that have a direct bearing on the discourses on electoral rules and policy evaluation, accessible to a larger audience. The text is essentially self-contained. No previous knowledge of mathematical logic or relational algebra is assumed. Whatever technical prerequisites are needed, are developed in the text itself. Although the text is at an introductory level, there has been no compromise on rigor. Unlike most introductory books, the relevant proofs are not omitted; rather, they have been explained in detail. The text has a large number of examples so that the concepts and results become clear to the reader. There is a large number of exercises with full solutions provided at the end of the text, so that the reader can check her/his understanding of the material.
Author(s): Satish Kumar Jain
Series: Springer Texts in Business and Economics
Publisher: Springer
Year: 2022
Language: English
Pages: 210
City: Singapore
Preface
Contents
About the Author
Abbreviations
Symbols
1 Introduction
2 Elementary Logic
2.1 Sentential Logic
2.1.1 Logical Connectives
2.1.2 Well-Formed Sentential Formulas
2.1.3 Tautologies, Contradictions, Contingent Formulas, and Logical Equivalences
2.1.4 Three Standard Proof Methods
2.2 Predicate Logic
2.2.1 Universally Valid Formulas
3 Sets, Relations, Functions
3.1 Sets
3.2 Relations
3.3 Functions
4 Binary Relations
4.1 Binary Relations and Some Important Properties
4.2 Some Elementary Propositions About Binary Relations
5 Social Choice Theoretic Framework and Arrow Impossibility Theorem
5.1 Social Choice Theoretic Framework
5.2 Arrow Impossibility Theorem
6 Some Important Value-Judgments, Rules and Theorems
6.1 Pareto-Optimality and Paretian Value-Judgment
6.2 Three Important Conditions on Social Decision Rules
6.2.1 Monotonicity Conditions
6.2.2 Anonymity (A)
6.2.3 Neutrality (N)
6.3 Characterization of the Method of Majority Decision
6.4 Pareto-Rule
7 Implications of Weakening of Some of Arrow Conditions
7.1 Implications of Weakening of Transitivity to Quasi-Transitivity
7.2 Implications of Weakening of Transitivity to Acyclicity
7.3 Acyclicity Under m-1m-Majority Rules
8 The Method of Majority Decision: Conditions for Transitivity and Quasi-Transitivity
8.1 The Reduced Form of a Profile
8.2 Necessary and Sufficient Condition for Transitivity
8.3 Necessary and Sufficient Condition for Quasi-Transitivity
8.4 Domain Restriction Conditions for Transitivity and Quasi-Transitivity
8.5 Latin Squares
8.6 Restrictions on Preferences
8.7 Domain Restriction Conditions for Transitivity and Quasi-Transitivity …
8.8 Single-Peaked Preferences
9 Strategic Aspects
9.1 Definitions, Assumptions, and Notation
9.2 Manipulability of Rules
9.2.1 The Two-Alternative Case
9.2.2 Manipulability of the MMD
9.2.3 The Plurality Rule
9.2.4 Manipulability of the Plurality Rule
9.3 Existence of Nash Equilibria
9.4 Existence of Strong Equilibria Under the Method of Majority Decision
9.5 Existence of Strong Equilibria Under the Plurality Rule
10 Summary and Concluding Remarks
Solutions and Answers to Exercises
Appendix References
Subject Index
