One way to hold this word: two sides are stuck, and a third person walks over, looks at the whole thing, and says how it goes. That person is not playing. They have no side to win for. Their job is only to look and to decide, and once they have decided, the matter is closed. Every use of arbiter keeps some part of that picture — the outsider whose word ends the question.
From the word’s history
Wiktionary traces arbiter to Latin arbiter, a witness or judge, literally one who goes to see. The picture of someone walking over to look, and then judging what they saw, sits right under the modern uses.
Wiktionary 記載 arbiter 來自拉丁文 arbiter，意思是證人、判斷的人，字面是「走過去看的人」。先走過去看，看過才判斷——這個順序，正好就是今天 arbiter 這個角色在做的事。
Wiktionary (kaikki:3f6f69a190036ae4:629375487:18396), etymology_text supplied in the evidence packet
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