It has happened in our history that there has been more than one slate of electors that purports to represent the state. The most famous example is 1876, when four states sent two slates of electors to Congress to be counted. But it also happened in 1960, when Hawaii sent more than one slate to be counted because a recount of a very close vote changed the winner from Nixon to Kennedy.
The 1876 incident inspired Congress to pass the Electoral Count Act of 1887 (“ECA”). That act aims to regulate the process of counting electoral votes. The ECA offers a procedure — complicated and incomplete — for determining which electoral votes will be counted.
The most important part of this procedure is the “safe harbor” provision of §5. (Note, we’ll refer to the current section numbers within Title 3 of the U.S. code, even though they weren’t the original section numbers. As we’ve said, Title 3 combines a bunch of statutes passed at different times.)
Under §5, in order for a slate of electors to qualify for “safe harbor,” the electors must be chosen according to the laws of the state enacted prior to Election Day (November 3), and any disputes related to the appointment of electors must be resolved at least 6 days prior (December 8) to the meeting of electors (December 14).
If between two competing slates of electors, one of them qualifies for “safe harbor” protection, then that slate of electors will be counted (unless both chambers of Congress reject the vote).
However, if there are multiple slates from a state that qualify for “safe harbor” protection, and if both the chambers agree to accept a particular slate, then that slate would count. Similarly, if both chambers agree to reject a particular slate, then that slate would not be counted.
If both chambers cannot agree to either accept or reject a slate, then the slate which was certified by the ‘executive of the state’ (generally considered the governor, but some interpretations would also consider Secretary of State to be an executive too – thus adding to the uncertainty) gets counted.