Domain Conditions And Social Rationality

Description

This book primarily focuses on the domain conditions under which a number of important classes of binary social decision rules give rise to rational social preferences. One implication of the Arrow and Gibbard theorems is that every non-oligarchic social decision rule that satisfies the condition of independence of irrelevant alternatives, a requirement crucial for the unambiguity of social choices, and the weak Pareto criterion fails to generate quasi-transitive social preferences for some configurations of individual preferences. The problem is exemplified by the famous voting paradox associated with the majority rule. Thus, in the context of rules that do not give rise to transitive (quasi-transitive) social preferences for every configuration of individual preferences, an important problem is that of formulating Inada-type necessary and sufficient conditions for transitivity (quasi-transitivity). This book formulates conditions for transitivity and quasi-transitivity for several classes of social decision rules, including majority rules, non-minority rules, Pareto-inclusive non-minority rules, and social decision rules that are simple games. It also analyzes in detail the conditions for transitivity and quasi-transitivity under the method of the majority decision, and derives the maximally sufficient conditions for transitivity under the class of neutral and monotonic binary social decision rules and one of its subclasses. The book also presents characterizations of some of the classes of rules for which domain conditions have been derived. The material covered is relevant to anyone interested in studying the structure of voting rules, particularly those interested in social choice theory. Providing the necessary social choice theoretic concepts, definitions, propositions and theorems, the book is essentially self-contained. The treatment throughout is rigorous, and unlike most of the literature on domain conditions, care is taken regarding the number of individuals in the 'necessity' proofs. As such it is an invaluable resource for students of economics and political science, with takeaways for everyone – from first-year postgraduates to more advanced doctoral students and scholars. Front Matter ....Pages i-xix Introduction (Satish Kumar Jain)....Pages 1-8 The Preliminaries (Satish Kumar Jain)....Pages 9-25 The Method of Majority Decision (Satish Kumar Jain)....Pages 27-52 The Strict Majority Rule (Satish Kumar Jain)....Pages 53-67 The Class of Semi-strict Majority Rules (Satish Kumar Jain)....Pages 69-92 Special Majority Rules (Satish Kumar Jain)....Pages 93-108 The Class of Strict Majority Rules (Satish Kumar Jain)....Pages 109-115 The Class of Pareto-Inclusive Strict Majority Rules (Satish Kumar Jain)....Pages 117-127 Social Decision Rules Which Are Simple Games (Satish Kumar Jain)....Pages 129-138 Neutral and Monotonic Binary Social Decision Rules (Satish Kumar Jain)....Pages 139-158 Quasi-transitive Individual Preferences (Satish Kumar Jain)....Pages 159-187 Summary and Concluding Remarks (Satish Kumar Jain)....Pages 189-193