On lambda-majority voting paradoxes

A new supplement to McGarvey's wellknown theorem is given. Namely, we prove that for each lambda with 1/2 < lambda < 1 there exists a tournament T on some finite set of alternatives A such that for every profile of A there ex ists an are (a, b) of T such that the proportion of voters that prefer to b is less than lambda. In other words, there exist tournaments that cannot b e a lambda-majority relation of any profile. Lower and upper bounds for the minimal majority with which we can generate all tournaments on n alternati ves are also given. (C) 1999 Elsevier Science BN. All rights reserved.