In this paper, we classify all maximal peak-pit Condorcet domains of maximal width for n ≤ 5 alternatives. To achieve this, we bring together ideas from several branches of combinatorics. The main tool used in the classification is the ideal of a domain. In contrast to the size of maximal...

We investigate the ways in which a linear order on a finite set A can be consistently extended to a linear order on a set Pk(A) of multisets on A of fixed cardinality k. We show that for card(A) = 3 all linear orders on Pk(A) are additive and classify them by means of Farey fractions. For...