In public parliance and stuff like those inane 'New World Order' conspirationite fears, there is one major yet discrete world organisation that seem rarely brought up - Interpol. Except maybe oddly in stuff like asian pop culture (was Bruce Lee helping an agent in one of his movie, and CHun-Li the Street Fighter an agent too?).
The organisation was created in 1923, wikipedia told me, and seem to a web of cooperations between national polices, helping to track down international criminals and organisations like the mafias, and seem not related to the UN.
So, how we can by example have NO Interpol up to 'now' (is it inevitable?)?
Maybe an harsher cold war, one side fearing that this Organisation is tied to 'capitalist fascist states' or 'red commies', and refuse to join by a certain isolationism, rendering it neutered partially? Or the links in WWII with Nazis are deeper, it get unmade?
What would be the conserquences on law enforcement and judiciaries of the world? The mafias and criminal cartels of the world are stronger, as there is quite less international cooperations?
OR an alternate Interpol, how and what? Maybe it is indeed a creation of one block, or a successfull and surviving Society of Nations? Or it is locked after WWII to the UN?