In the One World Government thread, I used the example of American evangelicals pushing Bush to cut federal funding to embryonic stem-cell research as a reason to be wary of a one-world government, where those with inconvenient ideas had nowhere to run.
That got me thinking...
So, with a POD no earlier than 1940, have a world government run by evangelical Christians. It need not be right-wing evangelicals--there are left-wing evangelicals as well, such as Tony Campolo. Campolo, for example, pointed out that although there are several Bible verses condemning homosexual behavior, there are a buttload more condemning the abuse of the poor.
Before you think this scenario ASB, there is a lot of Christian evangelism in "The Global South" and there's a book called The Next Christendom that suggests this is where Christianity will be strong in the future as Europe and North America secularize.