Which of these best describes the power of the House of Representatives in presidential elections?

The power of the House of Representatives in presidential elections is best described by the ability to decide the winner if the Electoral College fails. This scenario is specifically outlined in the U.S. Constitution. If no candidate receives a majority of electoral votes, the 12th Amendment stipulates that the House of Representatives must select the President from the three candidates who received the most electoral votes. Each state delegation in the House has one vote, which emphasizes the unique role that the House plays in ensuring a President is chosen if the Electoral College cannot fulfill its function.

The other options do not accurately reflect the House's powers. The House does not conduct nationwide voting sessions or directly elect the President. Also, appointing electors for the Electoral College is not a function of the House; instead, this responsibility is typically handled by state legislatures. The specific power to determine the outcome of a presidential election when the Electoral College is deadlocked highlights an important aspect of the legislative branch's role in the federal election process.