Ah, the Beauprez quandry. My suggestion is to vote with purity. The more who vote how they really want to see governed the greater the impact on policy. You do not ignore how say 15 or 18% of the electorate vote.

Since 1792 America has endured the:
Federalist, Democratic-Republican (Anti-Federalist), Jackson Democrats, Whigs, Democrats, Republican, and Progressive parties plus minor parties. They gained and lost power because voters accepted and then rejected the principles they stood for. I think the Republican party is on the way out since it no longer espouses any principles. Better to let it wither and die than encourage it with your vote. Vote your principles!

I vote on principles. I am told that I throw my vote away doing that, or that the really bad guy will win over the bad guy. I just keep in mind what Rearden said and change the wording a bit. Instead of 'Try pouring a ton of steel without rigid principles." I change it to "Try running a real republic without rigid principles."

Always vote according to your conscience and principles, otherwise you will end up feeling dirty. Well at least I do.

I agree with k. Purity in voting in a way is our simple form of parliamentarian coalition building. The politicians at least then have an idea where the public stands on an issue to a better degree.

Another pragmatic idea: Contribute to the principled candidate to raise the important issues. Go to the lesser-of-two-evils candidate's fundraisers and get to know their staff. When they're in office and an important bill comes up, they may remember you, esp if you sort-of made a connection in some way at the event. If you can reach that person, you can ask, "Remember how we talked about issue XYZ at the canddiate's b-day event. Is she going to support HRxxxx?" If hundreds of people do that, it puts huge pressure on the lesser-of-two-evils lawmaker.

It's not necessarily the most righteous approach, but I would vote for the lesser-of-two-evils candidate if I thought she/he had a close chance. If I thought it was going to be a landslide either way, I would vote my principles.
I wonder if instant runoff voting would resolve this dilemma.

A vote for a major party candidate is just another compromise, and every founding principle that made this nation great has been obliterated by a slow process of incremental compromise. Vote your principles; we don't move things our direction by compromising in the other direction.

I am heartened by the responses. So much so, that I have pointed everyone up. As I got ready to leave for the polls, I saw this atlas shirt in the drawer; "The evil of the world is made possible by nothing but the sanction you give it - John Galt.
Whether the greater evil or the lesser evil wins, I did not sanction evil today!