Suppose one coded a bitcoin variant that works as follows.
Difficulty still varies up and down to target a set number of block being generated in a set time period. However, the coinbase amounts are not following a hardcoded decreasing pattern to target a fixed final amount of issued currency, but are adjusting up and down to target a fixed exchange rate, for example pegging the currency to the dollar. (Please don't get stuck at this point on how undesirable this is, I'm not advocating for it, just trying to convince myself whether it would work.)
Exchange rate is determined by demand and supply. We have no control over demand but some control over supply (not perfect control, since we can't control when hoarders will choose to sell, but assuming some miners sell their coins soon after generation, we have control over this portion of supply). In order for the network to know what the coinbase amount for the next block should be it needs to know what the exchange rate is. Therefore the current exchange rate is also placed into every block. If the exchange rate in a block is incorrect for the time when the block was generated, the block is rejected. If the exchange rate goes above one (Fiatcoins become too valuable), then the coinbase transaction is increased and if it drops below one (Fiatcoins become too cheap) then the coinbase amount is decreased. This is analogous to a central bank increasing and decreasing the money supply via interest rates which in turn affects the exchange rate of the currency.
One important point is that this may well work, not because the feedback loop thus created is particularly effective, but because it creates an expectation of what the exchange rate "should be". If a large group of people believe that the exchange rate will tend to 1:1 in the long term they will buy when the rate dips below 1 and sell when it rises above 1. The built in mechanism can only affect the the exchange rate over long periods, but the expectation that the protocol will eventually force the rate back to 1 leads traders to keep the rate at unity, even in the short term.
Of course having the exchange rate in every block causes technical issues. If everyone is getting their rates from the same exchange, then the network has a single point of failure. If we get our rates from different exchanges, then as long as there is still a functional exchange somewhere that is reachable by most miners, the network remains functional. However, if miners are free to use exchange rates from any exchange, then I can't reject any block that has a price that doesn't match the price at my reference exchange exactly, since the rate may well be different at other exchanges. I can however reject anything that deviates by more than a small margin, since arbitrageurs should keep the exchange prices close to one another.
The power of expectations is unbelievable. Give people a plausible reason to believe that the exchange rate will tend to X in the long term and it becomes a self fulfilling prophecy. Another example is the bitcoin test network. On a technical level the test and production networks are indistinguishable (aside from scale), yet bitcoins are worth almost $17 dollars each (right now, who knows what they'll be worth in 5 minutes) while test network coins are utterly worthless. Why are they worthless? Because we expect them to be.
This messes with my mind
