Majorization and measures of classical polarization in three dimensions

There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the polarization state space in the process. We use majorization, previously used in quantum information, as a criterion to establish a partial ordering on the polarization state space. Using this criterion and other considerations, the most useful polarization measure in three dimensions is found to be one dependent on the Bloch vector decomposition of the polarization matrix.