If your vote has less value to you than the time it takes to cast the ballot, it has zero economic value, and will therefore not happen, regardless of its nonzero absolute value.
A cynical potential voter may recognize that the net effect of laws and rules set up around the voting system is to alienate his or her opinion from the results of elections. In that case, declining to vote is a rational and reasonable decision. Most people judge the value of their votes by the perceived impact that their votes have on the results of the election. If you cannot detect a change in public policy as a result of your votes, your vote does literally have zero value.
In that case, you should be doing something else to effect a change in your own situation. I suspect that for most people, working during the time you would ordinarily spend voting then spending the profits on a lobbyist to directly influence an already-elected policy-maker for a specific issue that interests you would be more effective than casting a free ballot.
The person who casts the deciding vote probably won't know that they had done it, so that vote could also have zero value. All they know is that the voted for the winner.
Every vote in the entire election could have zero value, if none of the winners change their political stances as a result, and public policy is essentially unchanged from the period before the election.
That's why I see votes on a binding referendum to have more value than races for office between two essentially indistinguishable candidates.
In U.S. politics (and I suppose generalizing to other majoritarian voting systems), the only realistic option for a major party shift to occur is a schism in the ruling dichotomy - as happened with the Whigs being torn on issues of slavery and fizzling out to Republican and Democratic. Or, more recently, the Southern Strategy morphing the Republican Party's platform into a more populist one, taking over the role of the Democrats prior to the 1960s, and dramatically transforming the formerly blue Deep South into a firmly red bloc.
Trying to break a third party in any other way is remarkably difficult, as a result of the inertia caused by reasons I listed previously. It's been engineered this way for well over a century by now.
Until you reform ballot access laws, introduce proportional representation on the federal and state level (which will break so much shit it's not funny) and have fairer debate coverage, trying to wrestle in third party candidates through mere vote will be exceedingly implausible/impractical.
Entryism, I suppose, is another option, though it has not been used effectively at all thus far.
Here's the thing with voting: the person with the most votes wins. Even if they're a third party candidate and even if they weren't "supposed" to win. I think this is a really cool!
There are examples of this happening. Surprise progressive wins. The system doesn't make it easy, but it's possible. It will happen again. But it's a whole lot harder when their supporters choose not to vote.
A cynical potential voter may recognize that the net effect of laws and rules set up around the voting system is to alienate his or her opinion from the results of elections. In that case, declining to vote is a rational and reasonable decision. Most people judge the value of their votes by the perceived impact that their votes have on the results of the election. If you cannot detect a change in public policy as a result of your votes, your vote does literally have zero value.
In that case, you should be doing something else to effect a change in your own situation. I suspect that for most people, working during the time you would ordinarily spend voting then spending the profits on a lobbyist to directly influence an already-elected policy-maker for a specific issue that interests you would be more effective than casting a free ballot.