Only in the federal elections for President of the United States can this occur, as the Electoral College vote outcome will supercede the popular vote's.
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
yes
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
23rd
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate.
Run-Off
Eugene V. Debs was the Socialist candidate who ran in the election of 1912 and won 6 percent of the popular vote.
It is possible that a candidate could win the "national" popular vote total but lose the electoral vote total. However, the electoral vote of every state accurately reflects the popular vote within that state. A candidate could win the electoral votes in a large state such as California winning the state by a huge margin. However, the opposing candidate could win the electoral votes in other states because a majority of the voters in those states vote for the opposing candidate. The President of the United States is the president for the people of all 50 states, not just the President for California, New York and a few of the other large states.
Barack Obama won the Popular Vote in the 2008 Presidential Election by about 8,500,000 votes.