Ordinal preference representations

Ordinal preferences have several advantages over the traditional cardinal expressions of preference. Three different representations of ordinal preferences useful in multi-participant modelling are presented, and their features compared. One approach is thepayoff representation that is based on an ordinal normal form game. A second representation of ordinal preferences is thepreference vector, based on the option form of the game. The option form consists of a list of players, with each player followed by the options under its control. The third representation of ordinal preferences is thepreference tree. A preference tree is an implied binary tree that captures the information of preference vector in a more compact manner by making use of its lexicographic structure. The preference tree offers considerable compactness and computational efficiency over the other two approaches.