This is a question every libertarian comes across at some point, if not repeatedly and ad nauseam. There are two answers to this question. The first is what I would term the moral or principled answer. Which is “We don’t care.” Let me explain that this way. Imagine we are living in the 19th century and as a party we advocate the abolition of slavery. An enterprise which has hitherto gone on unhindered for thousands of years. A concerned person may very well inquire “but who would pick the cotton?” Our answer would be “we don’t care”. This is your problem to overcome. But whatever solution you eventually apply, you cannot use slaves, as it’s a violation of an individual’s right to liberty and morally reprehensible.

Now back to our all important roads (or any other public service for that matter). Whatever solution you apply to the problem must not involve force or coercion. To take an individual’s property in the form of land or revenue without their express permission in order to carry out your project, no matter how well intentioned, is theft, a violation of their individual rights, and morally reprehensible.

Now we turn to what I would term the practical answer. Let me begin by first asking you a question. Who do you assume builds the roads presently? If your answer is “the government”. You are wrong. Currently, in the UK at least, private construction companies facilitate the building of roads. The government is merely the customer. A middle man, if you will. Between you, the financier, and the provider. In many instances the financier may not even desire or require the road, and may even be opposed to it’s construction. However, the government has decided in it’s infinite wisdom that you, the financier, require the road and a road you will get. Not only that, but you WILL pay. Even if the road fails to be completed on time and runs ruinously over budget.

Under a libertarian government, roads would continue to be built by private companies, but only on private contract between subscribers and providers. That way only those who want or need the road would be required to pay for it by toll or any other voluntary method.