The benefit of the electoral college is that the president-elect must seek out widespread support, and not just stack up large majorities in certain geographical segments of the country.
Sort of. It can also mean that the person that a majority wanted may possibly lose. While very far-fetched, the following is something that can theoretically mean a Democratic victory:
Democrat: 271 EVs, 28%
Republican: 268 EVs, 71%
At the moment, I can't think of a way to prevent both the possibility of a person winning with only a concentrated but super-strong base of support and the possibility of a person winning while the majority, or at least plurality, supported the other person. I'm not even sure if one exists, although I may delve into the question further now that it's been raised, as I feel it's an interesting one. It mainly depends, however, on which possibility you feel is the worst, with regards to which system you feel is better. There's no universally "best" system.
The other issue is this: suppose there was some mass exodus of people in the direction of, say, California and Texas, resulting in the following map:
This is obviously even more lopsided and clustered, but this is still nevertheless a 270-268 Democratic win, even though there is hardly any broad support whatsoever. Since the electoral college does take population into account, it does not
always require broad support. Even in the first example using the EV numbers as they were in 2004, broad support is not
really attained.
The other issue with the electoral college is stuff like the following. Here's the results from the 2004 election:
Shift only a few votes in one state and you get this:
Kerry still loses the popular vote by a considerable margin, but all of a sudden he's won the election. If you don't like the variance in only one state, then give Kerry a 1.11% swing nation-wide - the same effect happens, in which Kerry loses the popular vote but wins the election.
The electoral college has the tendency to really exaggerate state results - winning by only one vote means that you get everything and that the loser gets nothing, even though support in the state is, in reality, about dead even.