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A state doesn't really have control over the value of its currency. It may control how much of it exists in circulation. Likewise, the Bitcoin software tightly controls how much Bitcoin is in circulation. Both limits are done by fiat. Whether the institution doing the fiat is what you personally would recognize as a "state" seems to be a pretty arbitrary distinction. "States" are not the end-all be-all of institutions with power over individuals.

A state controls the money supply by granting itself a monopoly on money production (i.e. it outlaws the production of "counterfeit" money). Bitcoin uses a different strategy — while anyone is allowed to make bitcoins, the increasing production costs ensure there will only be a limited supply. At leasts that's my understanding of how bitcoin works. At any rate, none of this has anything to do with being fiat money. Fiat money means that the money is backed by "trust", i.e. people accept it as currency because they trust that others will also accept it.

"A state doesn't really have control over the value of its currency."

That's a wildly inaccurate statement. A fixed exchange rate, such as that imposed on the Chinese Yuan is a complete refutation of your claim.

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