Ozdemir, UgurSanver, M. Remzi2024-07-182024-07-1820070176-17141432-217Xhttps://doi.org/10.1007/s00355-006-0154-7https://hdl.handle.net/11411/7118We call a domain of preference orderings dictatorial if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as being essentially saturated, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated ( hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.eninfo:eu-repo/semantics/closedAccessSocial-Welfare FunctionsVoting ProceduresMajority-RuleStrategyExistenceTheoremsPrivateArticle2-s2.0-3375108718810.1007/s00355-006-0154-7761Q16128Q3WOS:000243378900004