This is inspired by a post by Ross Douthat on talk of running a third-party candidate if Donald Trump is the Republican nominee, with the goal of throwing the election into the House of Representatives. This would require winning some states that the Democrats would otherwise have won, which rules out a "movement conservative." Some people have proposed trying to do it through the Libertarian party, but Douthat points out that Libertarians have traditionally done better in the Mountain west, and that winning places like Wyoming or Idaho is going to take electoral votes away from Trump, not Clinton or Sanders. So what's left? Nobody asked me, but here's my advice.
Since 1980, the third-party candidates who have received the largest share of votes were John Anderson in 1980, Ross Perot in 1992 and 1996, and Ralph Nader in 2000. Although they represented quite different ideologies, there was a positive correlation between the state-level share of the vote for each one--that is, if one third-party candidate did well in a state, all third-party candidates did well. Here is a scatterplot of vote for Anderson in 1980 and Perot in 1996, which was the weakest of the correlations. There is a definite relationship: for example, Vermont (in the upper right) was a relatively good state for both Anderson and Perot, while Alabama (lower left) was a poor one.
I did a factor analysis to get a score which can be interpreted as disposition to support third-party candidates. The top-scoring states were Maine, Alaska, Vermont, Rhode Island, Montana, Massachusetts, Minnesota, Connecticut, New Hampshire, and Oregon. In 2012, those states had a combined total of 56 electoral votes, 50 of which went to Obama. So if a candidate won these states, there would be a decent chance of preventing the Democrat from getting a majority of the electoral votes.
But do those states have anything in common? I think Alaska and Montana are distinctive, but that the New England states plus Minnesota and Oregon share "good government" traditions, the sort of thing that was associated with moderate Republicanism back when moderate Republicans roamed the earth. So the most promising strategy for people who want to throw the election into the House of Representatives would be to run a moderate Republican, maybe someone like the former Senator from Maine, Olympia Snowe. If supporting an avowed moderate was too much for them, maybe they could call the candidate a "Reform Conservative."
[Note: it was surprisingly difficult to get data on vote shares by state in a convenient form. I finally found spreadsheets going all the way back to 1828, compiled by Stephen Wolf.]