This dissertation provides an investigation into axiomatic choice theory. Two distinct sets of results are presented. The first of these provides weakenings Hammond's characterization of Consequentialism to for allow for quasi-transitive rationalizability and acyclic rationalizability of choice functions. A set of results paralleling those already existing within the standard choice function consistency framework is thereby established In the second set of results presented, choice set based rankings over the power set are examined. Three axioms are provided which guarantee that a choice extension will be: (i) acyclic, complete and reflexive, (ii) quasi-transitive, complete and reflexive, and (iii) a weak ordering. A characterization result is provided for an intuitively appealing ranking over subsets known as the Q-Ordering
