Threshold aggregation of multi-graded rankings

A recent paper by Aleskerov et al. [Aleskerov, F., Yakuba, V., Yuzbashev, D., 2007. A 'threshold aggregation' of three-graded rankings. Mathematical Social Sciences 53, 106-110] characterizes so-called threshold aggregation rules of three-graded rankings in terms of four axioms Anonymity, Cancelation, Pareto, and Non-compensatory Threshold. In this paper we extend this result to the case of multi-graded rankings, and we provide an alternative characterization in terms of slightly weaker axioms.