Though I'm obviously rather interested in politics, I have not voted in any election since 1997.
I won't say that my reasons are particularly good ones, or all that consistent and defensible. But I'm not sure they're worse than most folks' reasons for voting either.
First, on a straight utilitarian calculus, voting is nonsense. The probability of decisiveness in any reasonably sized electorate makes voting less rational than buying lotto tickets if the point of voting is to get a better bundle of policies than you'd otherwise get. And I don't buy lotto tickets. Yes, we're all part of the equilibrium, and if I abstain, then the median shifts ever so slightly away from my ideal point. But it can't be by enough to induce me to vote at current turnout rates. The great strength of the median voter theorem is that it's robust to weirdo extreme preferences. But if I have weirdo extreme preferences, my abstention makes little difference to outcomes.
But even if turnout numbers were low enough that my vote were expectationally beneficial, on a straight utilitarian calculus, I'd still be really uncomfortable with it. Why? I'm too much of a contractarian at heart, and I don't like that politics has essentially unrestricted domain. There are large sections of my life, and of your life, that I don't believe should be subject to democratic decision-making. Regardless of what a majority wants, I think you should have the right to marry whomever you wish, to ingest what you like, to engage in whatever voluntary exchanges you like that don't infringe on others' property - in short, to pursue what you view as the good life so long as your enjoyment does not unduly infringe on the equal rights of others. And far too much of politics seeks to impose the majority's view of the good life on others.
I've a reasonable contractarian foundation. If I agree to a process, then I'm bound to accept the outcome of that process. And voting outside of a context where baseline rights are protected against majoritarianism means I give assent to the process that strips others of their rights, even if I voted against that outcome. It's not Sophie's choice, but it's not a good one.
I often hear arguments of the form "Well, if you don't vote, you can't complain." A contractarian of my stripe would reverse things: if you agreed to the rules of a poker game, you can't whine afterwards that you lost your shirt. If you don't like the game, you shouldn't play it at all: abstention is not unreasonable. If I vote, I give my assent to the idea that it's right that a majority should be empowered to deny a gay couple the right to full marriage, a cancer sufferer the right to pain relief through marijuana, a landlord to the right to his house should it be seized subsequent to a tenant's use of it for drug trafficking. It isn't just that I object to that those policies are the existing status quo but even more that they're inside the domain of politics at all - that it's considered right and proper that majorities should be able to decide these things.
Where do I think voting is right and proper? Let's start with easy cases. You join a club, which has limited purposes, with easy exit, and the club has to decide on something within the club's remit. I've voted in the various clubs to which I've belonged at one time or another.
I joined the economics department here at Canterbury 7 years ago. I vote on stuff in departmental meetings and at Faculty when it doesn't just pass by assent. The decisions are on matters that are within the proper remit of the club - I agreed as much when I joined the club - and I can always find another employer should the club's rules move too far away from what I'd signed on for.
Consider then the next step up: voting in a body corporate (condo association) in an apartment building. Their range of powers is typically limited, and you choose a body corporate based on the kinds of decisions it's empowered to make. That's pretty reasonable. If I were in a condo, I'd not be opposed to voting. I'd choose one where the body corporate's domain weren't too broad, and I'd vote.
Local body politics are the next step up. Non-voting in these elections is far more a function of expected low decisiveness than of philosophical objection. There's lots of stuff that city councils do that I don't like - the officiousness of swimming pool inspectors being high on the list - but they're typically restricted in domain not just by legislation but also by Tiebout competition. If I don't like Christchurch's policies, I can move to Rolleston or Kaipoi or Oxford. The restrictions that Councils tend to impose just can't infringe too much on heterogeneous visions of the good life. The majority of the decisions that City Councils make are properly the kind of things that ought to be decided democratically.
But I would get strong disutility of voting where the representative body has powers over domains that ought never be in the democratic realm. My voting then gives legitimacy to that those domains are subject to political rather than personal choice.
I'm sure that there's at least something, for each of you, that you'd consider absolutely to be in the realm of the personal rather than the political. Suppose you woke up tomorrow and found that elected representatives now decided who you would be required to marry. Some bureau would run matching algorithms and allocate partners. Would you be anti-democratic for thinking it abhorrent that we use democratic processes to allocate spouses? Suppose the two main candidates offered competing variants of the matching algorithm, and you knew one would yield a marginally better match for you. If you voted, you might be able to get a change in policy to improve the matching algorithm. If you got really really lucky, some third party candidate might get the policy liberalized to allow individual choice. But you'd have conceded that the dimension ought to be in the domain of democratic choice.
Suppose Kodos offers a bundle of policies that is very slightly more appealing on economic grounds than Kang and Kang offers a bundle of policies that is very slightly more appealing on civil liberties. Both promise to eat no more than a hundred tasty humans: Kodos will eat no more than a hundred drug users; Kang will eat no more than a hundred landlords. Voting for either, or for some no-hope third party candidate, kinda says you're OK with a system that winds up letting Kodos or Kang eat people so long as enough people vote for them. I don't think whether Kodos or Kang ought to be able to eat people should depend on how many people vote for them; I think rather it ought to depend on the preferences of those who would be eaten. Don't blame me: I didn't vote.
Bottom line: for national elections where I'm unlikely to affect the outcome but certain to experience strong disutility from voting at all, I abstain. If I expected that my vote had a really good chance of changing the outcome substantially - not just flipping things from National to Labour (or vice versa) but rather say in a binding referendum on a sharp civil liberties issue (neither Kodos nor Kang to eat more than 50 people instead of 100) where iPredict said it was a 50/50 proposition - I'd probably get out and vote. But I'd still need to have a shower afterwards.
This all was prompted by @LewStoddart pestering me about why I don't vote. I don't claim these reasons to be particularly convincing for anybody whose preferences are around the median - they couldn't be, because the median voter is by definition comfortable with that the kinds of things that are decided by politics are decided by politics. But they're convincing enough for me.