Let’s start with a quick definition. I'm defining government as a coercive entity that plunders wealth by force, and redistributes it on projects of various kinds, from infrastructure and bribing voters, to war and weapons of mass destruction. I am not talking about all systems of organization (as some people seem to define government that way). Therefore, firms can exist without a government, since people in firms earn their living by providing goods and services other people willingly pay for. They don't need to point a gun at anyone's head to earn a living.
The Engine of Self-Interest
As with all problems on a free market, the greatest (though not the only) engine of problem solving is self-interest. The farmer may have lofty goals of feeding others, but he's mostly there to earn a living for himself, and whether or not he wants to help his fellow man, on a competitive free market he must provide a good product at a good price or nobody will buy it from him. His ability to satisfy his own self-interest is therefore primarily guided by the satisfaction of the self-interest of others. Markets are therefore inherently altruistic.
So, let me quickly summarize the people who would have a very strong motivation to build roads. We will also look at the mechanisms they can employ to finance this road building.
Who Wants to Build Roads?
The Salesman
That supermarket you like to shop at? The clothes store at the mall? All the other sales establishments you visit? They all want you to be able to get to their store. Whether they're located in the middle of a city, or outside it at a discount shopping center, they're very much self-interested in you, their customer, being able to reach their store with whatever vehicle you choose to use. If enough of their customers use vehicles with wheels that their sales justify the building and maintenance of a road, then it will be built and maintained.
All Businesses
Every business has a logistical side to it. Whether it's the aforementioned stores needing to be restocked, a factory producing goods, a farmer raising cattle, or anyone else who needs something delivered to and from them. All of these people need roads (or railways) to get goods to and from their business. This is why most of the railways built in the United States were built privately - the businesses requiring them were more than willing to pay the railway companies.
By the way, I question very much if the current emphasis on trucks for transportation of goods would have occurred if the government hadn't externalized the costs of road building onto all taxpayers. If the people who used them most had to pay for them, railways might still be dominating roads for heavy logistics. I suspect railways are cheaper and more efficient for such purposes than highways, and that roads networks would mostly exist only in densely populated areas, with scarcely populated areas in between being connected by rail.
Shipping companies
If businesses are prepared to pay to have materials delivered to them, or products shipped away from them, then shipping and road-building companies will pop up around this demand, and create a market for it. Absent a government, existing companies like UPS, FedEx, DHL, and all the others, would have to allocate a sufficient part of their budget for road building and maintenance, or face losing their entire business.
Tourists
How much of the airports and airlines are built using money coming from tourists? Businesses are not the only ones who use transportation infrastructure. If demand from tourists is good enough to get huge flying metal constructs into the air, I'm sure people on a free market can handle fundraising for something as simple as roads.
The Homeowner
It's not enough for the businesses you patronize to have roads. You still need roads to leave your house and reach their roads, and that means building roads in neighborhoods. There are several ways this can be done.
The first is a public ownership project, in which each homeowner chips in and they collectively raise funds to build the roads. This system runs into the free rider problem - why should you pay for the road when you can just wait for your neighbor to do it? And of course while everyone thinks this way, the roads don't get built.
Here's where threshold pledge systems come in. The website kickstarter.com uses a system just like it. The rules are simple: An entrepreneurial fellow calculates the costs of building the road and starts a project. People can pledge their money with no risk to themselves, because unless the goal is reached, they are not charged.
Not only will the non-participant now gain nothing from his non-participation because he can no longer be a free rider and the road will simply not be built without sufficient funding, but anyone who doesn't participate when they have an actual need for the road (e.g. they have a car they can't currently use) will probably face social pressures from his community.
Interestingly, there can be competing offers. If someone else (such as a manager in a firm who build roads professionally) thinks they can build the road cheaper, they can compete with their own bid. Unlike a government system in which bureaucrats try to siphon off as much taxpayer money as possible, the mechanism here is reversed, as firms compete to build the road as cheaply as possible, while still maintaining good quality.
Now this is by no means the only way the road can be built. A private firm could buy the land, build a road, and deny access to it unless the user pays the construction and maintenance fee. In my opinion, this system is less likely to be as popular as the threshold pledge system because fear of abuse would prevent homeowners from selling their land for road use to such a company in the first place.
Perhaps the homeowner could rent out a part of his land for road use to a company, or even give it away for free on condition of perpetual permission to use the road, and the company would agree because they would be getting land for free, and would earn enough money from people outside the neighborhood using the roads to justify not charging the homeowner.
I'm sure there are other ways of raising funds I simply haven't thought of. It's also possible that a sufficiently profitable business will build and maintain a road all the way to the home owners, or that networks of roads will be funded by contributions from all the shops and offices whose customers and employees need them to get to work.
You know how some businesses advertize that a portion of their revenues goes towards medical research, and other charities? I can picture a sign saying "5% of all proceeds at this store go towards maintaining your local community road network." That way you can bring your custom to whichever business you feel supports your community the best.
One thing you should realize is that everyone is already paying for the roads. The question is not one of a lack of funding. If anything, given government inefficiency in the administration of taxpayer funds, on a free market people would pay much less for roads. More importantly perhaps, people would pay for roads largely in the proportion in which they use them. Transportation companies and car drivers would pay more for road maintenance than people who choose to walk everywhere.
I can imagine that a company would charge users differently based on the vehicle they use. A car obviously inflicts much more damage to a road than a bicycle, therefore requiring more maintenance. It also causes more congestion (unless the car's passenger seats are all filled). I expect car drivers would pay a lot more for the right to use a road than cyclists.
The Advantages
If roads were built on a free-market, with a diversity of competing builders and owners who had self-interest at their heart, we would have much safer roads, and with far fewer potholes.
Why? Simple: You have two roads you can take. The first is a road built and owned by company A, who has a time-tested reputation for good quality roads, and safe rules and regulations for their use. Not rules based on politics, but based on science and accident prevention. Their speed limits, use of signs, and other safety rules and devices are determined largely by an analysis of accidents, use of statistics, and a little motivation from insurance companies, who are more than willing to lower their premiums for a more safety-minded road owner.
Road B is built by a firm with a horrid reputation, run by incompetent and corrupt businessmen who resemble politicians more than anyone else. It is statistically more dangerous in use, its poor maintenance and potholes cause more damage to your car, and the rules that govern its use (set by the property owner) are frankly insane.
Which road will you choose? Which company will prosper, and which will soon go out of business?
On a free market, the answer is obvious. Under a government system, Road B and its company continue to prosper, for the simple reason that they don't ask you which road you want to patronize. They just point a gun at your face and take your money.
For example, in an excellent display of spontaneous order on a free market, experiments that switched off traffic lights in a city actually reduced congestion while improving safety, since drivers became a lot more attentive and careful. On a competitive free market, road owners and managers would constantly look for ways to improve the safety and efficiency of their roads, and successful experiments would be emulated by their competitors, rapidly spreading the implementation of innovative ideas.
One way funds could be raised is subscriptions. Road owners could charge a one-time fee for use of their road (such as by using tolls, or cameras photographing license plates and sending bills to their owners), or they could use the far more efficient subscription method. Using it, a driver can pay a yearly, monthly, or other fee and have access granted to the road for a period of time. To make things even easier, there are likely to be road networks, in which road owners enter their roads into a single network, and they are then paid a share of the subscription fees based on use of their roads.
Subscribers could attach small electronic devices to their cars, which would be scanned at regular intervals to allow passage. Although advancements in technology are opening up new ways with which to make roads that much more efficient, a tried and tested low-tech method used for hundreds of years has been turnpike roads and trusts.
I'm curious whether "Which road network are you subscribed to?" will become a standard question on insurance forms for car drivers - so you will have an additional monetary self-interest in choosing safer roads.
Extrapolation
Now for a mental experiment, try to extrapolate the kind of reasoning above to all the other goods and services you may think cannot be provided without a government.
Good stuff! I will cross-post it in a bit.
Regarding this…
"For example, in an excellent display of spontaneous order on a free market, experiments that switched off traffic lights in a city actually reduced congestion while improving safety, since drivers became a lot more attentive and careful."
have you heard of this?
https://christophercook.substack.com/p/increasing-freedom-make-people-nicer
(Note, the still image of the video makes it look like it's no longer working, but it is.)