SUPER ARROVIAN DOMAINS WITH STRICT PREFERENCES

Given m greater than or equal to 3 alternatives and n greater than or equal to 2 voters, let sigma(m,n) be the least integer k for which the re is a set of k strict preference profiles for the voters on the alte rnatives with the following property: Arrow's impossibility theorem ho lds for this profile set and for each of its strict preference profile supersets. We show that sigma(3, 2) = 6 and that for each m, sigma(m, n)/4(n) approaches 0 monotonically as n gets large. In addition, for each n and epsilon > 0, sigma(m, n)/(log(2) m)(2+epsilon) approaches 0 as m gets large. Hence for many alternatives or many voters, a robust version of Arrow's theorem is induced by a very small fraction of the set of all (m!)(n) strict preference profiles.