Yes, theoretically this could work. However, you are trading your vote. A vote is a sacred thing. Our forefathers sacrificed their lives so we would have democracy, which wouldn't exist without voting rights. Women and African Americans had to fight for suffrage.
Voting symbolizes freedom.
Freedom is no longer present in voting when you decide to vote for something that goes against your political beliefs. Vote swapping allows for further manipulation and corruption of the voting process. It also encourages vote selling and buying. Those that agree with vote swapping may say they are harmlessly trading, not selling, a vote. There are plenty of people in this country that simply don't care about the presidency, but would do anything for a buck.