CAIRO — By force of this year’s Arab revolts and revolutions, activists marching under the banner of Islam are on the verge of a reckoning decades in the making: the prospect of achieving decisive power across the region has unleashed an unprecedented debate over the character of the emerging political orders they are helping to build.

Few question the coming electoral success of religious activists, but as they emerge from the shadows of a long, sometimes bloody struggle with authoritarian and ostensibly secular governments, they are confronting newly urgent questions about how to apply Islamic precepts to more open societies with very concrete needs.

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