"Not voting is a statement."
A statement which nearly half of Americans make every election year, and one which Republicans at least view as a statement in support of them, as outlined here.

Voting 3rd party, even if your candidate is destined to lose, does have an effect on the elections and behaviors, though. Because in an attempt to win your vote next election season, the parties move towards the largest 3rd party votes. Example, Ron Paul last election had a huge following and many of those who supported him voted third-party when he wasn't nominated. One of his largest platforms was being an outsider who would affect real change. Look at the platforms of candidates this election cycle. Trump and Sanders both ran on a similar platform looking to gather the vote of Paul supporters from the year before. It's almost like third party votes act as a feedback mechanism, eh?