Cosmetic X is one of the most preferred cosmetics from this survey if and only if S(X,Y) ≥ S(X,Y) for every Y other than X. You note that it has been known for this type of surveys that there always exists at least one cosmetic that is preferred the most.

이 문장의 밑줄 친  S(X,Y) ≥ S(X,Y)가  S(X,Y) ≥ S(Y, X)로 수정되어야 하는 것 같습니다.