Acyclic and indifference-transitive collective choice functions.

Arrow\u27s classic theorem shows that any collective choice function satisfying independence of irrelevant alternatives (IIA) and Pareto (P), where the range is a subset of weak orders, is based on a dictator. This thesis focuses on Arrovian collective choice functions in which the range is generalized to include acyclic, indifference-transitive (ACIT) relations on the set of alternatives. We show that Arrovian ACIT collective choice functions with domains satisfying the free-quadruple property are based on a unique weakly decisive voter; however, this is not necessarily true for ACIT collective choice functions where Arrow\u27s independence condition is weakened. For ACIT collective choice functions with linear order domains, we present a complete characterization, as well as a recursive formula for counting the number of Arrovian ACIT collective choice functions with two voters