Majority Decisions and Transitivity: Some Special Cases

Abstract

The problem considered is that of obtaining majority decisions which are transitive. We show that the corresponding optimization problems for the weighted l1 norm and the weighted l2 norm are identical. We then show that she general problem of minimizing the weighted lk norm can be equivalently formulated as a set covering problem. Finally, we identify the Tchebycheff problem (l2 norm) with a class, of bottleneck quadratic assignment problems and give an efficient algorithm for solving it.