Does a cryptocurrency that can have its supply be reduced based on some factor currently exist?
If not, is this possible? If so, how?
This is possible through the use of a multiplier. For example, you could add it to Bitcoin as follows:
You add a "currency multiplier" and "next currency multiplier" to the block header.
All Bitcoin amounts presented are multiplied by this multiplier.
You have a set of rules for how the next currency multiplier changes. For example, miners could be permitted to change the "next currency multiplier" by a small amount in each block.
Periodically, say every time the difficulty is adjusted, the currency multiplier is also adjusted by up to 2% (or whatever) towards the next currency multiplier and the next currency multiplier is set to the new currency multiplier.
So if I want to pay you "1 Bitcoin", I actually have to pay you an internal amount that depends on the multiplier. Changes in the multiplier would change everyone's displayed balances. This way, if miners believed there were too many Bitcoins in circulation and the value was dropping, they could "vote" to reduce the multiplier. This could result in a more stable price and thus make it easier to price goods in Bitcoins. At least, those would be the arguments in favor of such a scheme.