Preference diversity orderings
Applying new preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (Soc Choice Welf 41(4):965–988, 2013) criterion is developed. It is shown that all previously used indices violate this criterion. Two new indices (geometric mean-based and leximax-based) that satisfy a new criterion are developed. Leximax-based orders act as a polarization index and are compared to the polarization index of Can et al. (Math Soc Sci 78:76–79, 2015). New impossibility results are obtained.