The formal selection of the nations president?

The group that makes the formal selection of the nations president is called the Electoral College.

In the U.S. The United States Electoral College is a group of electors established by the United States Constitution, constituted every four years for the sole purpose of electing the president and vice president of the United States. The Electoral College consists of 538 electors, and an absolute majority of 270 electoral votes is required to win an election.