People think that it is unbelievable if a presidential candidate wins in the electoral college but has 5 to 10 percent LESS popular vote. This definition shows an absurd and extreme, but illuminating example of how the loser in the presidential election can have an arbitrarily high percentage of the popular votes compared to the winner, i.e., way more then 5 or 10 percent.
Suppose there are 540 electoral votes. Divide the states into two groups, one having 271 votes, the other 269. Suppose in the "271" states, only 1 person in each state votes Democrat, 0 Republican. Suppose in the "269" states, 0 vote Democrat, millions Republican. Then by the electoral college majority, the democrats win but the Republicans have a million times more votes than the Democrats.
In the 2012 presidential election, it initially appeared that we might have an electoral college paradox. But the Democratic popular vote came back up and it was avoided.