This paper first reviews the different dominance criteria that have been proposed in the literature in order to obtain robust bipolarization orderings. We notably contrast dominance criteria related to indices based solely on the distribution of distances from the median, and dominance criteria for the wider set of indices where these distances may not be given the same weight depending on whether they refer to the bottom or the top half of the distribution. In order to increase the set of tools for bipolarization orderings and increase the ordering power of dominance tests without having to impose this neglect of the relative position of each observed income with respect to the median, we also propose sequential dominance criteria that makes it possible for increased distances below (or above) the median to be compensated by reduced distances above (or below) the median, but not vice-versa