Cubic preferences and the character admissibility problem

The notion of separability is important in a variety of fields, including economics, political science, computer science, and operations research. Separability formalizes the idea that a decision-maker’s preferred ordering of outcomes on some dimensions within a multidimensional alternative space may depend on the values of other dimensions. The character admissibility deals with the construction of preferences that are separable on specific sets of dimensions. In this paper, we develop a graph-theoretic approach to the character admissibility problem, using Hamiltonian paths to generate preference orderings. We apply this method specifically to hypercube graphs, defining the class of cubic preferences. We then explore how the algebraic structure of the group of symmetries of the hypercube impacts the separability structures exhibited by cubic preferences. We prove that the characters of cubic preferences satisfy set theoretic properties distinct from those produced by previous methods, and we define two functions to construct cubic preferences. Our methods have potential applications to a variety of multiple-criteria decision-making problems, including multiple-question referendum elections.