The phrase "ultimate arbiter" means the final or highest authority that makes decisions or settles disputes. It is the most powerful and influential entity that has the final say on a particular matter. Full definition
Above all, faculty members, no matter how competent and distinguished, need to guard against the ever present temptation to set themselves up as ultimate arbiters in their special fields, thus stifling any efforts by their students to become truly critical and original. (religion-online.org)
The market will be the ultimate arbiter, as it always is. (inc.com)
Chip: You'll know it when the founder of the company is the ultimate arbiter for every question. (inc.com)