@article{c9ce50f98d33422b93b763d7c05684f2,
title = "Collective rationality and dictatorship: The scope of the arrow theorem",
author = "Blair, \{Douglas H.\} and Pollak, \{Robert A.\}",
note = "Funding Information: We know only one proposition in the literature concerning social preferences satisfying rationality requirements which lie between Arrow{\textquoteright}s weak order and Sen{\textquoteright}s quasi-transitive order: Both Brown [6] and Wilson [19] assert that the dictatorship result holds when social preferences are semi-orders. However, as Blau [3] observes, Brown does not offer a proof of this assertion and Wilson{\textquoteright}s proof is incorrect. Since, as we shall show, the Arrow result does hold for semiorders, Sen{\textquoteright}s claim that “Arrow{\textquoteright}s result hinges crucially on the requirement of full transitivity...” [16, p. 3881 is not true. Brown and Wilson do not attempt to characterize the class of rationality requirements which lead to dictatorship, nor to indicate the breadth of the class. Our results imply that there is a sensei n which any rationality requirement stronger than quasi-transitivity implies dictatorship. Our proof of this result is straightforward, having the sames tructure as the standard proofs of * Pollak{\textquoteright}s research was supported in part by the National Science Foundation. We are grateful to Julian H. Blau, Eric S. Maskin and Chester Spatt for calling our attention to errors in our earlier draft, and to Rajat Deb for helpful comments. 186",
year = "1979",
month = aug,
doi = "10.1016/0022-0531(79)90012-7",
language = "English (US)",
volume = "21",
pages = "186--194",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",
number = "1",
}