What is excludability?
David Henderson critiques Mankiw's exposition of excludability. Mankiw uses public roads as an example of non-excludable goods. Henderson argues that the non-excludability of public roads is an artifact of the legal arrangement in which the government makes it illegal to exclude others from using public roads. This implies that non-excludability is not some inherent property of roads. Henderson further argues that the definition of excludability is not a legal one. He uses Samuelson's definition where a good is non-excludable if "there are no low-cost ways of excluding people". From this, Henderson concludes that excludability is a technological characteristic of goods. Goods are then non-excludable because some of their technological characteristics that make it too costly to exclude others from using them.
I am sympathetic to Henderson's aim of pointing out the distinction between technical and legal aspects of excludability. However, if the definition of excludability is that "there are no low-cost ways of excluding people", I would not limit the definition to being only a technological one. The cost of available technologies depends on the value individuals within society ascribe to them. So, for example, if it is technologically possible to exclude someone, but people choose not to because it is too expensive, that means excludability is not only a technological characteristic, but also a characteristic that depends on preferences. Subjectivists like Ludwig von Mises would probably go even further and claim that it is entirely up to our preferences whether or not something will be a low or a high cost alternative because preferences determine value.
Another issue to consider is that the legal environment and cost can't be disentangled. Costs of performing various exclusion activities depend on our expectations of what other people consider as an acceptable exclusion technique. My cost of excluding someone from driving my car is different in a society that adheres to the property rights regime compared to a society in which property rights violations are seen as nothing to worry about. In a society that punishes property rights violations, I may not have to invest as much in protecting my car from theft compared to a society in which car theft is something people accept as normal. For an example of a society in which car theft was a normal everyday event, one can just go back to my home country, former Yugoslavia, in the 1990s.
So, we have to conclude then that, to define a benchmark for excludability, we need to assume a specific legal arrangement in which people operate. Then we can look at the technical properties of different goods and how people value those technical properties. Since people are free to form their values as they wish, excludability and non-excludability of different goods will ultimately depend on people's values, expressed within a given legal framework.