According to the economist George Stigler, politics is far from a winner-take-all game.
Source: Is a Vote for a Third Party Really a Waste? - FEE
I've been a third party voter, especially when it comes to presidential elections, for a long time. Generally, I'll vote for the Libertarian candidate but not always. I often here that a vote for a third party is a wasted vote or a vote for the "other guy" but who the "other guy" is depends on the politics of the person I'm talking to. As if it is a vote for Schrodinger's Cat or something.
I realize, of course, that the third party candidate isn't likely to win. However, it is the mindset that "third parties can't win" that ensures that third parties can't win. I won't be a part of it. If I hate both candidates from the two main parties, I see no reason to vote for either one of them. When more people join me, perhaps something will actually change. Until then, we'll only get more of the same. While the rhetoric seems different at times, the policy differences between Democrat and Republican are more alike than they are different. At least for the issues I care about most. For example, I want a party that will reduce spending, reduce taxation, and simplify the tax code. Neither major party will do any of those things. I also want a party that cares about civil liberties. Neither party does.
Also, it doesn't necessarily take a 3rd party victory to influence policy. If a third party starts to gather even a little more support than in the past, you can bet that one of the major parties will start incorporating some of those ideas into their platform. It will make a small difference to be sure but honestly, I think that's potentially a bigger difference maker than choosing a democrat or republican. Even if it's not, the difference a Republican or Democrat winning makes isn't big...or positive. Just slightly less negative in some ways and slightly more negative in others with an emphasis on "slightly".
There's a joke I like to tell. It's not really that funny but it's true. Do you know what I hate most about Democrats? They make me want to vote for Republicans.
That isn't to say that there are no good Republican or Democrat politicians. There's occasionally a few of them out there. But they don't tend to make it to the presidential level.