Six days after Bryan's post, commenter GregS made an important point that I fear will get lost in the shuffle but is important enough to share. It expresses my view of voting. Here it is:
Suppose that by not voting you're setting a bad example for your audience. A number of young, impressionable people see your talks or read your blog and are convinced by your arguments. But they are then put off by your refusal to vote. Some of them remain fully convinced of your arguments, but you persuade them not to vote. And some decide that you're just not serious if you're not putting forth the tiny effort required to vote, so you lose them completely. I want to ask how many such people would there need to be to convince you to vote? Is there a number? A single vote is small, but a room full of voters could sway an election, particularly at the local and state level.
In this same vein, consider "Don't vote but tell people you do" as an irrelevant third option, one of those tricks from behavioral economics where nobody really wants the third option but it makes the chooser flip their selection. (The other options being "vote and tell people you vote" or "don't vote and tell people you don't vote.") You'd nudge policy in the libertarian direction if your "example" convinced a few hundred libertarians to vote, but I suspect your conscience would nag you. I think you'd like to have the example-setting benefits of voting along with the "trauma"-sparing benefits of not voting, but your conscience wouldn't allow you to be that dishonest.
If you're an influential opinion leader, voting isn't just about your single vote. It's about setting an example.
When I posted about my view of voting on Facebook, there followed an interesting discussion in which one FB "friend" (I don't actually know him but we are friendly) suggested that I actively try to get out the vote, for reasons GregS discusses above, but that, if asked whether I vote, say Yes even if it's a lie. I told him that I refuse to lie. Not in all cases. (SS man: Are the Jews in your basement? DRH: No.) But in the vast majority of cases. If you think voting is traumatizing, try lying. So GregS's comment above is a propos.
Incidentally, I spent a large part of my day yesterday shooting a couple of 30-second ads that ideally will be used in California on a particular proposition on the ballot. (I would name the proposition but I don't want to use EconLog to appear to be advocating one way or another on a particular vote.) In one of the alternate endings--I don't know which one will be used--I said "Join me in voting No on . . ." It would be weird, and really pretty awful, to say that and then not vote.