Domain Conditions and Social Rationality

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The book delves into the conditions under which various binary social decision rules produce rational social preferences, highlighting the implications of the Arrow and Gibbard theorems. It discusses the independence of irrelevant alternatives and the weak Pareto criterion, revealing that many non-oligarchic rules fail to ensure quasi-transitive social preferences due to configurations of individual preferences. The text also addresses the famous voting paradox linked to majority rule and seeks to establish necessary and sufficient conditions for achieving transitivity in social preferences.