Decision making is considered if there are multiple numerical criteria. An original general approach to solving multi-criteria problems is outlined in the presence of quantitative information on the preference of the decision maker (SCL). The four axioms of "reasonable" choice are considered fulfilled. The concept of a quantum of information about the SCL preference is introduced. The question of narrowing the Pareto set based on a finite set of information quanta is investigated. It is shown that using the proposed approach, it is possible to approximate quite well the set of potentially optimal solutions to the multi-criterion problem. Tasks with both clear and fuzzy preference relationships are considered. The possibility of combining the axiomatic approach with other known methods is being studied.