Majority-consistent preference orderings

This paper considers the construction of sets of preferences that give consistent outcomes under majority voting. Fishburn [7] shows that by combining the concepts of single-Peaked and single-troughed preferences (which are themselves examples of value restriction) it is possible to provide a simple description of the extent of agreement between individuals that allows the construction of sets that are as large as those previously known (for fewer than 7 alternatives) and larger than those previously known (for 7 or more alternatives). This paper gives a characterisation of the preferences generated through these agreements and makes observations on the relation between the sizes of such sets as the number of alternatives increases.