That’s not a tacit assumption, but one that have been observed in a number of settings.
Andreas
11

You have spoken about what Nash’s argument is but you have not quoted what you assert he said and I do not agree with your implication and claim to this regard. Here is an example that support’s the idea that ultimately the purpose of (good) money is not at all necessarily for the use of the average citizen:

In a large state like one of the “great democracies”it is reasonable to say that the people should be able,in principle, to decide on the form of a money (like a “public utility”) that they should be served by, even though most of the actual volume of the use of the money would be out of the hands of the great majority of the people. But most typically the people would expect to be served by their elected representatives and not to make most of the relevant decisions in a direct fashion.

In regard to Metcalfe’s law:

The Myth Of Metcalfe’s Law

Here is the law:

Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (n2).

But we quickly gain clarification:

First formulated in this form by George Gilder in 1993,[1] and attributed to Robert Metcalfe in regard to Ethernet, Metcalfe’s law was originally presented, c. 1980, not in terms of users, but rather of “compatible communicating devices” (for example, fax machines, telephones, etc.).[2]

Metcalfe’s law does not state in any way that if you add users to a network then the value, and therefore the price, increases. This would be an absurd claim and the analogy that comes to mind is an increasing population full of infants using fax machines.

Metcalfe rather speaks to POTENTIAL value, if we are going think about the price and market cap of a network. That is to say that there is room for matchmaking connections for N² users, but there is nothing in such a law to suggest that any amount of users can efficiently use a certain network (later in this writing we will read Szabo alluding to such redundancies).

In other words it cannot be said that the addition of each user adds the same amount of value which is then multiplied across the network. In most cases it is probably easier to show such a claim cannot be true (how much value would be added from the last person in the world to have a fax network?).

Here we get Szabo’s extension of Metcalfe’s law in regard to emerging economics (through Adam Smith):

Metcalfe’s Law states that a value of a network is proportional to the square of the number of its nodes. In an area where good soils, mines, and forests are randomly distributed, the number of nodes valuable to an industrial economy is proportional to the area encompassed. The number of such nodes that can be economically accessed is an inverse square of the cost per mile of transportation. Combine this with Metcalfe’s Law and we reach a dramatic but solid mathematical conclusion: the potential value of a land transportation network is the inverse fourth power of the cost of that transportation.

Notice Szabo’s use of the word “potential”.

Wiki supports these points:

In addition to the difficulty of quantifying the “value” of a network, the mathematical justification for Metcalfe’s law measures only the potential number of contacts, i.e., the technological side of a network. However the social utility of a network depends upon the number of nodes in contact. If there are language barriers or other reasons why large parts of a network are not in contact with other parts then the effect may be smaller.
Metcalfe’s law assumes that the value of each node n is of equal benefit.[6] If this is not the case, for example because the one fax machines serves 50 workers, the second half of that, the third one third, and so on, then the relative value of an additional connection decreases. Likewise, in social networks, if users that join later use the network less than early adopters, then the benefit of each additional user may lessen, making the overall network less efficient if costs per users are fixed.

Lastly it is not necessarily true that adding users increases the value, and more importantly it is not necessarily true that it is the only way or best way or most valuable path for bitcoin.

Bitcoin serves as a digital gold because it is strong by the characteristics Nash explains gold is valuable for, the Nashian sense of good, which he describes in great detail and nothing you have said speaks to.

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