Contingent Election of the President and Vice President by Congress: Perspectives and Contemporary Analysis [Updated October 6, 2020] [open pdf - 1017KB]
From the Introduction: "The 12th Amendment to the Constitution provides backup, or standby, procedures by which the House of Representatives would elect the President, and the Senate the Vice President, in the event no candidate wins a majority of electoral votes. Although this procedure, known as contingent election, has been implemented only once for each office since the amendment's ratification, the failure to win an electoral college majority is theoretically possible in any presidential election. Some contingencies that might lead to an electoral college deadlock include  an election that is closely contested by two major candidates, leading to a tie vote in the electoral college;  one in which multiple candidates gain electoral votes so that no candidate wins a majority; or  an election where a number of electors sufficient to deny a majority to any candidate votes against the candidates to whom they are pledged. Any one of these developments would require Congress to consider and discharge functions of great constitutional significance. Moreover, the magnitude of these responsibilities might well be further highlighted by the fact that an electoral college deadlock would arguably lead to a period of protracted and contentious political struggle. This report examines constitutional requirements and historical precedents associated with the contingent election process. It also identifies and evaluates contemporary issues that might emerge in the modern context."
CRS Report for Congress, R40504
Congressional Research Service: https://crsreports.congress.gov/