An Example There are lots of ways to get an outcome where the popular winner is the electoral loser. Here's just one simple example. Suppose we have just four states, but they vary in population. One candidate could win the medium sized states by a wide margin and barely lose the big and small states. That candidate would win the popular vote but lose the electoral college vote, as in this table where each winning total is in blue.
Combinations abound where a candidate can win the electoral race without winning the popular race.
The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves. The President of the Senate shall, in the Presence of the Senate and House of Representatives, open all the Certificates, and the Votes shall then be counted. In every Case, after the Choice of the President, the Person having the greatest Number of Votes of the Electors shall be the Vice President. But if there should remain two or more who have equal Votes, the Senate shall chuse from them by Ballot the Vice President. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.