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Yes the Arbiter respects John, in HALO 2 though the Arbiter hated the Chief and even called him demon, however that changed in Halo 3. Due to the fact that Elites and Humans are allies after the Covenant betrayed the Elites, the Chief and the Arbiter had to fight together, both of them didn't like that, in the beginning they even wanted to kill each other. From that point both of them were fightning together, and they started respecting and supporting each other.

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