Since Cato is a nonpartisan think tank, you won't see our scholars offering any recommendations on how to vote. But this seems like a good time to throw out some general considerations regarding whether and why to vote.
Many libertarians take the position that, because any one individual's vote is vanishingly unlikely to swing a national election, it's simply always irrational to cast a ballot---except perhaps in very small local races. I'm inclined to agree with my colleague Tim Lee that this is wrong, and even somewhat morally obtuse: There are many types of cases where a good social outcome depends on members of society being morally disposed to act according to a general norm, but where any individual's defection from the norm makes no significant difference to the outcome, and may be in some way slightly better for the defecting individual. Conspicuously, with the exception of very large donors, contributions to nonprofits like Cato are one such case! Adding or subtracting $100 from Cato's annual budget probably does not appreciably alter what Cato is able to do in a given year---but we are extremely fortunate that so many people who can afford $100 donations make them, since together they make a great difference indeed. And I assume they do this not only because they like getting a printed copy of Policy Report and discounts in the Cato Store, but because even the most strident individualist can appreciate that moral action sometimes involves thinking in terms of what we together do, and refusing to free-ride on the willingness of others to contribute to achieving important shared goods.
This reasoning undermines the "no marginal difference" argument that one ought never to vote, but neither does it entail that one is always morally obligated to vote. (I won't object if readers want to infer that it means they're always obligated to donate to Cato.) As Jason Brennan argues in his fine book The Ethics of Voting, one certainly ought not to vote just to have voted, without being well-informed about the candidates and the likely effects of their policies, and indeed, in this case, one would be morally obligated to refrain from voting. More generally, when we consider the effects of what we do together, we often find that the norms we ought to follow are complex and conditional, not crude categorical commands. We'd all starve if nobody engaged in agriculture, but it does not follow in a modern market economy that everyone must therefore engage in agriculture when we can instead reap the benefits of division of labor coordinated by the price system. And in many cases involving ordinary social helping---as when a pedestrian drops a stack of important papers on a windy day---we should hope bystanders regard assistance as an imperfect duty, so that some people spontaneously choose to stop and help, but not everyone, since for a large group of bystanders this would be wasteful and likely even counterproductive.
When and under what conditions one should be prepared to contribute or vote, and with what frequency or probability, is going to be an individual judgment call depending on a host of circumstantial and idiosyncratic factors, among which is one's estimate of what others in the relevant local area are likely to do. For a particular person, these may end up weighing in favor of seldom or even never voting in practice, or making it a habit to vote annually. Everyone should reject the argument for categorically abstaining on the grounds that one's vote makes no marginal difference---which betrays a failure to grasp that the decision involves moral norms governing collective action, akin to boasting that one never tips at out-of-town restaurants, because it's economically irrational---but, having rejected it, it does not follow that everyone should follow the same uniform rule about whether and when to vote. Relevant factors might include the expressive value one gets from voting generally, one's attitude toward the choices in a particular race and the local issues on the ballot, and whether one lives in a "battleground" or "safe" state.
If one does decide to vote, there's the further question of how one ought to vote in our first-past-the-post, winner-take-all voting system, in which the victor is typically sure to be from one of the two major parties. Here, again, we tend to see a stark contrast between advocates of categorical or pure strategies: those who insist one should always "vote one's conscience" irrespective of the chances of victory for the ideal candidate, and those who urge a "pragmatic" vote for the least bad of the major party candidates. Both of these pure strategies, however, have problems.
As leftist blogger Daniel Davies pointed out in a 2010 post at Crooked Timber, the "pragmatic" argument employs a concealed bait-and-switch: First, it employs an appeal to civic duty in order to persuade those repulsed by the "lesser evil" candidate that they must hold their noses and trudge to the polls even though their individual vote isn't going to decide the election. Then, it shifts to a strategic argument for not casting a third-party vote even if that is one's first preference, given that the vast majority of other Americans will be voting for one of the major party options, and the consequences of letting the "greater evil" win are too dire. In other words, it urges the moral necessity of disregarding the fact that other people's votes will determine the election when deciding whether to go to the polls, but taking into account what's known about how others will vote when deciding how to cast one's ballot.
The "always vote your conscience" rule has its own issues. If you take the injunction seriously, and believe that you ought to vote for the ideal candidate regardless of their chances of victory, you'd probably most often cast a write-in ballot, rather than voting for either a major party or a third-party candidate. Yet if everyone did this—at least under our electoral system—a small number of voters with a shared first-preference could perversely select a victor far lower in the preference rankings of the vast majority than any number of compromise candidates, in an extreme version of the "spoiler effect."
As with many thorny problems in ethics, this one comes down to appropriately specifying the scope of the group for whom you're trying to formulate a general rule of action. The logic of the democratic process is inherently both collaborative---we together decide our future---and conflict-oriented, since it assumes disagreement about what course of action would best. This suggests that the appropriate way of approaching electoral choice, then, is neither at the level of purely individual economic rationality (which would tell you to stay home) nor the society-wide level of a truly universal categorical imperative. Instead, I'd propose that one should act on the imperative one would give to the intermediate-level (and admittedly fuzzy) group of citizens of the same state who share your basic political commitments, and so are wrestling with similar alternatives.
For a libertarian, this might mean others for whom the Libertarian Party candidate Gary Johnson is the closest match, but who are tempted to support whichever of the major party candidates they dislike least. What if all those people---a minority, but perhaps a significant one---voted the same way? In states where that voting bloc could swing the contest between the major party candidates, preventing the "greater evil" outcome might take priority. In states that are a virtual lock for one or the other, one might think the best use of that bloc's votes was a strong symbolic showing for the candidate most aligned with the common values that define the subgroup.
This is hardly a complete solution, of course: I've stipulated one way of choosing a subgroup as the subject of the general rule on which one acts, when there are many dimensions on which voters could be divided into different groups. Still, framing the problem in this way seems like a potentially promising starting point for grappling with the ethical quandaries of voting.