In this thesis we develop a new method for constructing binary preference orders for given interdependent structures, called characters. We introduce the preference space, which is a vector space of preference vectors. The preference vectors correspond to binary preference orders. We show that the hyperoctahedral group, Z2 o Sn, describes the symmetries of binary preferences orders and then define an action of Z2 o Sn on our preference vectors. We find a natural basis for a preference space. These basis vectors are indexed by subsets of proposals. We show that when completely separable binary preference vectors are decomposed using this basis, basis vectors indexed by nontrivial, even sized subsets do not appear in the decomposition. We then use these basis vectors as building blocks for preference construction. In particular, we construct preference orders whose Hasse diagram of separable sets have a tree structure
