It's not even a stamp of approval for the electoral system itself. If you pay me $X, but I believe that you owe me $Y >> X, I don't relinquish my claims to the remaining amount by taking what's currently on the table, unless I claim that I consider the debt settled. Same thing here - you can vote within the existing system without accepting the full legitimacy of that system. You're only accepting the limited power that your voice has in that system as a small part of the greater power that you believe you're owed.
Vote the vote that has the best chance of improving (or screwing up less in this case) whatever you care about.
Next election, politicians look at past elections. They look at what percentages each candidate got, they analyze that based on each platform, the numbers, the demographics of each state and what they voted for.
By voting for a candidate, i'm adding to the number of people that voted for them. I'm becoming part of that statistic. So i'm going to use that statistic to my advantage to get my voice heard. I'm going to vote for someone I actually believe in, even if they won't win. Then next time, at least those numbers are on the table. Maybe the next candidate will consider that by supporting "platform Y" they can get a percentage of those votes, and maybe i'll eventually have someone I support.
There doesn't seem to be a lot of evidence for this? In 2012, the GOP did a huge study on why they lost and came to the conclusion they needed to court minorities. Not only has that not been attempted by the Presidential nominee, but it's failed at the congressional level too. As for third-party candidates, it's not clear what effect Perot, Nader and others have had over the years beyond helping elect Bill Clinton and W.
A large third-party vote this election is almost certainly going to be a reflection on the likability of the two main candidates, and not on their policies. Meanwhile the risk that our country could be substantially worse off in the meantime is real, and there's precedent for that.
During the primary candidates don't have the luxury of the middle - they need to find a large enough group of support that can push the party in some direction that's going to get widespread party approval while trying to find a candidate that still has a chance at winning the election.
If you don't want to vote for president then at least go vote for the many other things that will be decided that day!
I guess it depends on whether you're looking at it from the short-term or long-term.
By voting for a candidate, i'm adding to the number of people that supported them. I'm adding to the number that can be looked at later to see what the american population supports. I'm adding to the percentages that will alter what future politicians will base their platforms on.
I can't do that when I don't believe in the vast majority of what either of their platforms are based on. So I'm not going to vote for either of them.