This paper surveys approaches to preference diversity measurement. Applying preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (2016) criterion, is developed. It is shown that all previously used indices violate this criterion. Two new indices (geometric mean based and leximaxbased)are developed that satisfy a new criterion. Leximax-based orders act as a polarization index and are compared with Can et al.’s (2015) polarization index. The paper concludes by formulating a new open question: the preference profile reconstruction conjecture.