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How likely is it that the seat of the League of Nations would move from Geneva to Constantinople? That said, I don't know of a better location for the World Moot than the Intercontinental City. (And I'm not the only one, see links below.) Certainly, it would give the Entente greater incentive to resist Turkish independence, at least in the Zone of the Straits.
Between Russian and Greek immigration to the City, and just plain prestige, what would be the effects of such a move to internationalize and cosmopolitanize this new Byzantium?