When you say something is left to discretion, you mean that it is left to the judgment and decision-making ability of an individual. Synonyms for this phrase include "up to the individual", "subject to personal judgment", "dependent on one's own decision", and "at the discretion of the person involved". All of these phrases convey the idea that the decision is in the hands of the person making it, without any external influence or direction. This level of independence can come with both benefits and drawbacks, as it allows for individual creativity and decision-making, but also means that there may be a lack of standardization or consistent direction in the decisions that are made.