But they may not immediately see why "the State" that they can imagine is a unicorn. So, to help them, I propose what I (immodestly) call "the Munger test."
Go ahead, make your argument for what you want the State to do, and what you want the State to be in charge of.
Then, go back and look at your statement. Everywhere you said "the State" delete that phrase and replace it with "politicians I actually know, running in electoral systems with voters and interest groups that actually exist."
If you still believe your statement, then we have something to talk about.
This leads to loads of fun, believe me. When someone says, "The State should be in charge of hundreds of thousands of heavily armed troops, with the authority to use that coercive power," ask them to take out the unicorn ("The State") and replace it with George W. Bush. How do you like it now?
If someone says, "The State should be able to choose subsidies and taxes to change the incentives people face in deciding what energy sources to use," ask them to remove "The State" and replace it with "senators from states that rely on coal, oil, or corn ethanol for income." Still sound like a good idea?
How about, "The State should make rules for regulating sales of high performance electric cars." Now, the switch: "Representatives from Michigan and other states that produce parts for internal combustion engines should be in charge of regulating Tesla Motors."
While I agree with these insights, and try to apply them fairly rigorously to things protected Constitutionally (such as free speech or freedom of conscience exercises), I think the explicit value of public choice theory is to be skeptical of the efforts of the state or those proclaiming the need for a state to intervene. And not to immediately and reflexively eliminate it. While that elimination may be desirable in its own ends, for a variety of public choice and private goods problems that are better left to markets to resolve (most forms of occupational licensure for example), I'm not convinced that this is an argument that libertarians should be advancing as the main goal when arguing with people who believe in unicorns.
Here's a simpler argument to evaluate:
1) Establish publicly what it is you hope to accomplish using state action. What is the actual problem we are hoping will be resolved or reduced. Presuming this is not Constitutionally restricted ("I want to shut up people with whom I disapprove or disagree!", "I want to require people to worship in the same way as I do"), we can proceed further.
2) Describe why this cannot be resolved without the intervention of the state (why do we need a law for this instead of leaving people to their own devices?, or otherwise expressed as "is this actually a/the problem?") And also by what mechanism the state will do so. If it is unlikely the state will adopt the general outlines of the mechanics you desire, are you aware why this is so?
3) Construct a mechanism that allows for the results to be evaluated, showing that it reduces problem X (or at least that problem X is being reduced). If people are unwilling to do this when they are discussing policy, they are not actually interested in doing #1 and we should require additional information as to their intentions (eg, this is where the "corn ethanol" subsidies come in, or the "WMDs" in Iraq.) Note: it is very difficult to separate state actions from those of the public or market responses in many cases. In some cases it is obvious what has done the lion share of work, in others the state's actions spawn public or market responses of their own that are "unintended" consequences. Nevertheless, we should want some method of evaluating simply whether the intentions of the policy are matching up with the effect, or whether the intentions have other goals in mind that are undeclared.
A large portion of public policies proposed, enacted, or supported after the fact (by conservatives or liberals) fail on this sort of cost-benefit analysis to show they are achieving some putative goal. Drug use is pretty consistent. Abortions have been declining as a procedure for well over a decade despite being legal (suggesting bans have little effect), and declining more in states and legal regimes that are less restrictive on sex education and especially birth control than in states that are imposing onerous and wasteful regulatory burdens on the procedure (waiting periods, parental consent laws, ultrasounds, etc). Various gun control regulations constantly proposed have little or nothing to do with the underlying violence in our country and its cities and towns. Militarized police forces and deployment of equipment have little to do with the level of violence and its accompanying risk to police or the public safety within a given community. "Stop and frisk" searches don't find many guns. And so on.
I noticed a lot of these philosophical problems during the lead up to the PPACA being enacted. We were told the problem was lots of uninsured people lacking access to quality health care. I am dubious this was the actual problem, for many reasons on its own merits; lots of uninsured people were transitory, many were "young invincibles" with limited need for health insurance, etc. But primarily I think it was a symptom rather than a causal agent. I saw two bigger problems at work; employers providing health care insurance instead of wages or other benefits (vacation time or family leave for instance), leading to the lack of an effective individual market for insurance, and rising health care costs owing to third party payment structures and an accompanying lack of transparent pricing. We sort of dealt with the latter problem and the rise of health care costs has started to slow over the last few years. It is unclear if this was achieved by legislation however and not simply a decline in incomes leading to substitution effects (for example, people self-medicating with alcohol or drugs, that prescription drug crisis didn't come out of nowhere) or people not consuming health care because of diminishing purchasing power from income stagnation or diminished savings, and so on.
The former problem meanwhile reared its ugly head again in the form of contesting birth control mandates already. And more pressing, continues to be a problem for people in between jobs, or who have lower quality insurance provided and cannot get or afford better insurance they may desire, or who have insurance that is well above their demands or needs provided (which in turn leads to overconsumption of health care since those lost wages can only be consumed by taking health care as payment).
I also encounter this frequently in calls for foreign interventions. I'm not sure what precise mechanics sending bombs and rockets and troops abroad establishes the goals that people proclaim (spread of democracy!, end to internecine conflicts caused by years of enmity and strife!). I'm skeptical that sanctions usually achieve much (see: embargo, Cuba). And so on down the line. What I am not saying is that we should do nothing, or that any and all diplomatic or military efforts will be fruitless and counterproductive, but I don't automatically agree we can do something about every problem on the globe and I do not automatically agree that since we "should do something", whatever someone proposes as a bold plan of action is that something. I'd like to know if it has some chance of success, or if it has a history of working, and so on. I apply that same skepticism to the public machinations of the state at home. Maybe the state can do something, if imagined "perfectly". If we have to imagine a perfect state to do it, it probably isn't going to get done though. What we need is things that can be imagined as "good enough", and if those are effective enough, easy to implement, transparent to evaluate, and do not cost exorbitant sums in taxation and relative individual autonomy, then they're probably fine. Markets at some level require and imply the existence of a state (who else may grant and enforce property rights and general laws in a less arbitrary way if not a third party?). Perhaps a much smaller one than the one we have, but a basic state is in there somewhere to grease the wheels of trust and transaction costs. What that does not imply is that anything and everything the state does is automatically legitimate and good.