See this interesting article at Fairvote, about a letter written by former President James Madison in 1823, suggesting a different way to choose the president. The article has a link to Madison’s letter. Madison wanted to give each congressional district one electoral vote. Also he wanted to end the system under which, when no one gets a majority of the electoral college vote, the House elects the President, with one vote per state.
Madison wanted to change the electoral college to give each elector two votes for President, a first choice and a second choice. And he believed that if no one got a majority, with either the first or second choice votes, then the entire Congress should choose the President, with each member of each house of Congress having one vote.