Let there be two owners A and B of commodities x and y, respectively, of whom A wants y and B wants x. With no money and no third commodity, the only way for both owners to obtain their desired commodities is directly from each other:
A --> y | B --> x
x _____ | y
y _____ | x
Otherwise, A and B must delegate their commodity ownership to someone who then redistributes it between them. A centralized approach, though, would at least in part contravene that ownership by transferring control of the system away from its legitimate owners. Hence, only a decentralized solution can preserve the whole commodity ownership underlying this exchange, by A and B exchanging x and y directly.
Direct commodity exchange still has two issues, either of which would be sufficient to stop it. The first problem has a subjective nature:
- To be exchangeable for each other, x and y must share the same exchange value.
- It can happen that every exchangeable quantity of x has a different exchange value to that of any exchangeable quantity of y.
Instead, the second issue is purely objective. Let (as below) A, B, and C own commodities x, y, and z, respectively. If A wants y, B wants z, and C wants x, then direct exchange could not give those three owners their desired commodities — as none of them owns the same commodity wanted by who owns their wanted one. Moneyless exchange now can only happen if one of those commodities becomes a multiequivalent: a simultaneous equivalent of the other two commodities at least for the owner who neither wants nor owns it — whether the other two owners also know of this multiequivalence or not. For example, A could obtain z in exchange for x with C only to give it in exchange for y with B, this way making z a multiequivalent (as asterisked):
A --> y | B --> z | C --> x
x _____ | y _____ | z*
z* ____ | y _____ | x
y _____ | z _____ | x
Still, this individually-handled multiequivalence poses a second pair of problems:
- Contradictory indirect exchange tactics are made possible. In this last example, A could still try to obtain z in exchange for x with C (only to give it in exchange for y with B) even with B simultaneously trying to obtain x in exchange for y with A (only to give it in exchange for z with C).
- By relying on more exchanges between various pairs of commodities, it not only allows for the mismatch to occur more frequently but also allows for all mutually exchangeable quantities of two commodities to have different exchange values.
Social Multiequivalence
Fortunately, all those problems have the only and same solution of a single multiequivalent m becoming social, or money. Then, commodity owners can either give (sell) their commodities in exchange for m or give m in exchange for (buy) the commodities they want. For example, again let A, B, and C own commodities x, y, and z, respectively. Still assuming A wants y, B wants z, and C wants x, if now they only exchange their commodities for that m social multiequivalent — initially owned just by A — then:
A --> y | B --> z | C --> x
x, m __ | y _____ | z
x, y __ | m _____ | z
x, y __ | z _____ | m
y, m __ | z _____ | x
With social (rather than individual) multiequivalence:
- With any number of such owners, there are always two exchanges for each commodity owner (who either sells or buys it before buying or after selling another one, respectively).
- All commodity owners trade a common (social) multiequivalent, which eventually goes back to its original owner.
Furthermore, even if all mutually exchangeable quantities of two commodities have different exchange values, these two commodities will still be mutually exchangeable if the social multiequivalent (money) is divisible into small and similar enough units. For example, let two commodities x and y be worth one and two units of a social multiequivalent m, respectively — x(1m) and y(2m). Then, let their owners A of x and B of y be also the owners of three m units — 3m — each. If A and B want y and x, respectively, but always exchange their commodities for m units — x for 1m and y for 2m — then:
A --> y _ | B --> x
x(1m), 3m | y(2m), 3m
y(2m), 2m | x(1m), 4m
Finally, since social multiequivalence makes commodity exchange always possible, as only money can, every social multiequivalent is money, which is, in turn, any form of social multiequivalence.
Money as Decentralization
However, historically, money has become more centralized as a result of coming under the control of governments, despite the decentralized ownership of commodities being preserved during their exchange. Indeed:
- It must preserve the same decentralized ownership.
- For it to be shared by all owners of commodities, it must be concrete.
However:
- It must be privately controlled by a public authority, whether it be over buying, selling, creating, or destroying it, due to its concreteness to each of those owners.[1]
- Its original intent is defeated because its then-centralized control prevents it from still representing a decentralized commodity ownership, at least in part.
Fortunately, despite necessarily concrete to all people, or socially concrete, a monetary representation can be rather abstract to each person, or individually abstract. For example, cryptocurrencies — like Bitcoin — use public-key cryptography to simultaneously represent money as a private key and this private key as a public key, so money becomes metarepresented, or metamoney. Then, despite remaining socially concrete as a decentralized network, any such metarepresentation of money becomes individually abstract as a monetary — meta — unit, which preserves its decentralization, by preventing any public authority from privately controlling it.
- For more information, see Metamoney: Abstractly Represented Money.