He actually was elected.
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According to the Confederate States Constitution, the President's office was almost entirely the same as that of thePresident of the United States. The President was to be:
chosen by an electoral college from each state in the Confederacy. Each state had as many electors as they had members in the Confederate Congress (senators + representatives). The only CSA presidential election took place on November 6, 1861, when electors for the electoral college were chosen in each state. Davis, who was already in office by action of the Confederate Congress, was elected president without opposition (receiving all 109 electoral votes)