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...

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters of a society belong to this set, their majority relation has no cycles. We observe that, without loss of generality, every such domain can be assumed to be closed in the sense that it...

In this paper, we classify all maximal peak-pit Condorcet domains of maximal width for n È 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...