Calculating the minimal fraction of thepopular vote to win the U.S. Presidency in the electoral college

As is known, in U.S. presidential elections, all 50 states and the District of Columbi(DC) award their electoral votes to (the electors of) U.S. presidential candidates based on the popular vote received by (the electors of) the candidates there (although two different schemes of awarding the electoral votes are currently applied in the U.S.). For each particular (expected or actual) voter turnout in each of the states and in the District of Columbia, one may need to calculate the minimal fraction of the nationwide popular vote that secures the winning of the U.S. Presidency in the Electoral College. It is shown that this fraction can be found from solutions to certain integer linear programming problems.