This is why we also need to be able to rank candidates in order of preference.
Or have a runoff.
I know that ranked choice voting/instant runoff voting/single transferable vote/whatever you want to call it seems like it would have all the benefits but none of the flaws of actually holding a runoff, but it doesn't.
Here is a simple example, Obama and Romney are running as usual and Ron Paul throws in his hat as well. Obama and Romney finish first and second in some order while Paul takes up the rear. I would venture that a majority of Paul's voters have Romney ranked second. In an instant runoff, Romney is the president. Would Romney have won a straight up contest between the two? Maybe, maybe not, we'll find out on Tuesday.
Here is a more complex example that shows why the system sucks. John, Dick, and Harry are all running. John is a hardcore Republican. Dick openly admits he is a socialist. Harry is an independent and everyone loves Harry. If Harry had taken either party's nomination he would have been assured of a majority in any election system. Unfortunately, because each party's base goes for John or Dick, Harry comes in third. If we are going to use second choice votes to decide the election, why are we eliminating the man who is ranked second on EVERY SINGLE BALLOT that he isn't ranked first on?
Now I know that a runoff would not solve the problem, everyone but the top two candidates would be eliminated. But, since no one is proposing using a system where someone could be everyone's second choice, no one's first choice, and still win, having a second vote would at least allow people to reevaluate their options. The first round becomes a primary election, you vote for your best candidate. The second round becomes a clear choice, which of these two guys, one of whom will win, is best.
For the record, I only think executives and U.S. senators should be elected like this, everyone else should be chosen by proportional representation. I also know that runoffs have lower turnouts. People should have the right not to vote.