Sophisticated preference aggregation

A Sophisticated Social Welfare Function (SSWF) is a mapping from profiles of individual preferences into a sophisticated preference which is a pairwise weighted comparison of alternatives. We characterize Pareto optimal and pairwise independent SSWFs in terms of oligarchies that are induced by some power distribution in the society. This is a fairly large class ranging from dictatoriality to anonymous aggregation rules. Our results generalize the impossibility theorem of Arrow (Social choice and individual values. Wiley, New York, 1951) and the oligarchy theorem of Gibbard (Intransitive social indifference and the Arrow dilemma, University of Chicago, unpublished manuscript, 1969). This paper is part of a project entitled “Social Perception—A Social Choice Perspective”, supported by Istanbul Bilgi University Research Fund. We extensively benefited from our discussions with Salvador Barberà, Herve Moulin and William Zwicker. We also thank Fuad Aleskerov, Sergei Artemov, Goksel Asan, Burak Can, Murat Ali Cengelci, Gabrielle Demange, Bora Erdamar, Doruk Iris, Ozgur Kibris, Semih Koray, Ipek Ozkal-Sanver, Rohit Parikh, Maurice Salles, Norman Schofield and an anonymous referee for their valuable contributions at various occasions. Last but not the least, Remzi Sanver acknowledges the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).