The Voter Basis and the Admissibility of Tree Characters

When making n simultaneous decisions (for example, in a referendum election), our preference for the outcomes on one subset can depend on the outcomes on a disjoint subset. A subset S is separable when the reverse is true: our preference ranking on the outcomes of S are independent of the other outcomes. The admissibility problem asks which collections of subsets can correspond to the separable sets of some preference order. We use linear algebraic techniques to construct a preference order whose separable subsets have a tree structure with respect to subset inclusion.