This argument, on the other hand, is just the madman theory of negotiation. Which unfortunately has been getting a workout when we're talking about the American political system recently. It isn't, like, wrong, but it's also kind of risky, especially given that your leverage as a voter is only one vote wide in the first place. Madman negotiating works better when you have a bomb, not just a gun pointed at your own head.
There was a piece I read a very long time ago that discussed the effects of non-voting or protest voting which I can't seem to find now. It illustrated the futility of the idea by pointing out that election results are binary -- you either won or you didn't, and the motivations of your voters are largely opaque, and the non-voters even more so because you can't even exit poll them. It talked about how politicians don't chase missing voters from the previous election, they always chase engaged voters for the next one, and the history of voting from the last election is nothing more than a starting point for them to start building a new platform based upon current trends. Any "message" a protest voter wanted to send is never received, since it is essentially a lack of information, and new votes are earned by responding to the to the people who are actually making noise now. Electoral politics is always played out in the present tense. What issues won or lost a previous election could do the opposite in a new cycle, but the only way to know is to observe the electorate as it is, not speculate as to what would have won last time.
Perhaps the closest analogy is the economic concept of the sunk costs fallacy. Once a vote is cast, it can never be uncast, and therefore has no purpose in being part of the next round of decision making. Politicians are going to focus on the next batch of votes they can win, and aren't going to spend time reading tea leaves about votes they didn't get from people who didn't express their desires before they voted.
This comes back to, once again, the fact that general election voting is
not political activism. Who you vote for in the booth will never be known to anyone, nor will your reasons why. It does not send a message, it only helps decide which of two policy platforms will be implemented for the next term. Voting is the very last part of the democratic process, where all the politics have been boiled down to a simple choice of governance. All the important activism stuff happens beforehand, in the streets, in the primaries, in talking to candidates and fellow voters. Once that's all over, there's just two choices, A or B. One of them is certain to be chosen, and depending on your political views, one will be overall better for you and one will be worse. Either you vote for the one that's better, or you make the one that's worse mathematically more likely. It's cruel, but that's how our system is. I don't like it either, but nobody else is bringing out guillotines yet, so it's all we've got.
Now, like someone else mentioned,
threatening a lost vote does exert pressure, but following through on the threat is worthless. This is because voting is anonymous. The candidate has to act on the threat because they have no way to know if you'll follow through on it, but since they will never know if you followed through on it or not, actually not voting just serves to hurt yourself. Sunk costs fallacy again. You can't undo the names on the ballot that is the end result of all the political activism. You can't use your vote to change the policies of the candidates. If they get elected, they'll work to enact the platform they ran on. If they don't, the next time they run they'll build a platform based on what people are looking for at the time. Your vote can never change any of that. All it can do is determine which of two policy platforms get enacted right now. One of them will be better for you than the other. That's it.