The phrase "final arbitrator" means the last person or thing that decides or settles a disagreement or dispute. It is the ultimate authority or judge in resolving a conflict. Full definition
At the end of the day, science is not at all the sort of final arbitrator which the law would wish it to be, and the weighing of truth comes down to the common sense of the judge and the jury. (newscientist.com)
Or should Parliament have the final word on what is negotiated, thus placing itself as the final arbitrator of the National Interest, which is «sort - of» what May appears to concede? (blog.politics.ox.ac.uk)
If getting the «traditional» stamp was the final arbitrator of «quality» and «marketability» than every book would earn out and every author would be able to quit their day jobs. (fantasy-faction.com)