Dictatorial domains in preference aggregation

We 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. * Department of Economics, Istanbul Bilgi University; [email protected] and [email protected] 1 This paper has been presented at the Second World Congress of the Game Theory Society, 5-9 July 2004, Marseille; the Seventh Meeting of the Society for Social Choice and Welfare, 21-25 July 2004, Osaka and the 27 Bosphorus Workshop on Economic Design, 21-28 August 2004, Bodrum. We thank Fuad Aleskerov, Göksel A an, Eyal Beigman, Semih Koray, Levent Kutlu, Francois Maniquet, Ipek Ozkal-Sanver, Pelin Pasin, Alper Nakka and John Weymark for their useful comments. Our participation in these meetings has been possible thanks to the financial support of the Turkish Academy of Sciences and the Faculty of Economic and Administrative Sciences of Bilgi University. Our research is part of a project on Electoral System Design which is financed by Bilgi University Research Fund. Of course, the authors are the sole responsible for all existing errors.