Domain Conditions and Social Rationality

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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…

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