Duverger's Law states that a plurality voting system (like ours, with one vote per voter, most votes wins) greatly encourages two overwhelmingly dominant parties, resulting from, for example, Libertarians and pinko commies like me voting for more-electable candidates even though other candidates better represent our views.
For the great number of us who feel more passionately about one issue or another, our system forces them into one or the other party, which has lots of other views which our votes support. Pro-life voters are pressured to support waterboarding and corporate tax cuts, while supporters of unions vote for Obamacare and gun control.
With only two choices, a fair degree of cognitive dissonance might arise. A voter who on their own would hold one position or another might find themselves conflicted after years of voting for candidates who hold the other position. To avoid the cognitive dissonance, they might begin to soften/change their views. In a system with multiple parties (or a system where the voting system doesn't so strongly discourage multiple parties), voters are more free to think for themselves.