CAIRO (CNN) - As Egyptians cast ballots Sunday in the second and final day of a runoff that will decide the country's first popularly elected leader, questions swirl about whether the military will actually relinquish power.

The runoff is taking place against a backdrop of political chaos: Egypt has no constitution and no parliament, following a court ruling just days before the runoff that invalidated an Islamist-dominated legislative body and then saw the military swiftly move to dissolve it ahead of the election.

Even the choice of candidates in the runoff appeared to reflect the political polarization spurred by the chaos: Mohamed Morsi, backed by the once-banned Muslim Brotherhood, and Ahmed Shafik, who served as the last prime minister in the waning days of Hosni Mubarak's regime.

The two-day runoff that began Saturday followed a May election that failed to produce a winner with a clear mandate.