Explain the role of the electoral college in electing the US president, and compare two instances, one from the 19th century and one from the 21st century, in which the president was elected despite a discrepancy between the popular vote results and the electoral college results.

The electoral college consists of 538 electors, who choose the president of the United States. These electors are sent from the states, in proportion to their population, and in all states except for Maine and Nebraska, the electors are bound to the candidate that obtains the plurality of votes in the state.

Some presidents have been elected despite having lost the popular vote.

An example from the 19th century is Rutherford B. Hayes, who lost the popular vote to his contender, Samuel J. Tilden, but still won because he got 20 more electoral votes.

An example from the 21st century is the most recent election: Donald Trump lost the popular vote to Hillary Clinton, but won the electoral college (304 votes vs Clinton's 227 votes). In part this is because Trump won several crucial states by very small margins, for example, Michigan, Wisconsin and Pennsylvania.