The term 'assign to a lower position' can be summarized by three words: RELEGATE, DEMOTE, and RANK. RELEGATE is an 8-letter word meaning to assign to a lower position or to send away to a lower place. DEMOTE is a 6-letter word meaning to reduce in RANK or to assign to a lower position. RANK is a 4-letter word meaning to assign a position in a hierarchy or to arrange in order of importance. All three words refer to the act of assigning someone to a lower position in a hierarchy.