There are various ways to describe how a decision or result was reached. Some synonyms for "were determined by" could include "were influenced by," "were governed by," "were dictated by," "were specified by," "were guided by," "were shaped by," "were decided by," or "were established by." All of these phrases imply that an external factor or set of factors had a significant impact on the outcome. It can be useful to have a range of synonyms at one's disposal in order to vary one's phrasing and avoid repetition in communication.