Preference profiles sustaining Arrow's theorem

Summary. Arrow's theorem is proved on a domain consisting of two types of preference profiles. Those in the first type are “almost unanimous": for every profile some alternative x is such that the preferences of any two individuals merely differ in the ranking of x, which is in one of the first three positions. Profiles of the second type are “appropriately heterogeneous”, with preferences similar to those generating the “paradox of voting”. Received: March 9, 2000; revised version: June 7, 2001