Compulsory voting seems rather obvious: the US is supposed to be run by majority rule. But with election turnout rates running between 40% and 60%, a candidate can take power with as few as 20% of the people voting for him (50.1% of 40%). By requring people to vote*, we guarantee that the winner of the election will have been chosen by the will of the majority.
*:If voting is compulsory, there will have to be a penalty for dodging one's civic duty. Since there always seem to be problems getting people to fulfill another civil duty, serving on trial juries, it would seem that a "one month or one trial (longer than a month)" jury service penalty would neatly solve both problems.