Following questions are related to a crypto project I am working on and proper answers are of utmost importance to this concept's development. I unfortunately lack expert knowledge about money supply mechanisms and quantitative easing. What mostly affects possibility of cryptocurrencies becoming worldwide-accepted money, beyond technical issues, is their inherent instability to fiat currencies, which renders them useless for everyday common transactions - because their price fluctuates so much (mostly because of speculation) and nobody trusts fluctuating unit-of-exchange.
So, in a fiat world when the buying power of money is decreasing, central bank expands money supply by simply printing more money (or rather they "create money" in exchange for government bonds as far as I know) and if the buying power of currency unit is increasing, central bank decreases money supply by selling bonds for money.
Now in cryptocurrency world similar approach recently resurfaced (just as an idea now, I don't know of any working implementation). It uses something like "seigniorage shares". Basic idea is we want 1 unit of cryptocurrency to be worth 1 USD. So the proposed solution in situation when we need to decrease the money supply (1 unit of cryptocurrency is worth more than 1 USD) then the system, working like central bank will create out of nothing some seignorage shares and sell them for investors hoping the system will buy them back in future for more cash, with profit for investor. Reversing this, if system needs to increase money supply (1 unit of cryptocurrency is worth less than 1 USD) it will buy those seignorage shares from users in exchange for units of that particular cryptocurrency. So far, it works like central bank.
But in cryptocurrency world, in theory, there exists another, more straightforward approach. We could just measure the price of 1 unit of cryptocurrency in comparison to USD and increase or decrease money supply by just simply increasing or decreasing balances of cryptocurrency's account-owners pro-rata. So basically, if we need to put 10% of total cryptocurrency units out of existence to regain peg 1Crypto: 1USD, we could shrink all account balances by 10%, simply. And if we need more units in circulation to regain peg, then we increase all account balances pro-rata. It seems like it would work and it would work like central bank.
But bank uses shares as an instrument to take money and give money. One of the cryptocurrency experts Robert Sams wrote in his paper (https://bravenewcoin.com/assets/Whitepapers/A-Note-on-Cryptocurrency-Stabilisation-Seigniorage-Shares.pdf):
"How not to distribute One simple solution is to distribute pro-rata over all coin balances. This is the approach advocated by Ametrano in his creative coin stabilisation scheme dubbed ”Hayek Money”. This approach has the virtue of simplicity. All wallet balances are simply multiplied by Qi/Qi−1 in each period to arrive at a new wallet balance. [...] The problem is that this scheme only stabilises coin price, it doesn’t stabilise the purchasing power of a wallet balance. Recall the three functions of money: 1. Unit-of-Account 2. Store-of-Value 3. Medium-of-Exchange Price stability is not only about stabilising the unit-of-account, but also stabilising money’s store-of-value. Hayek money is designed to address the former, not the latter. It merely trades a ﬁxed wallet balance with ﬂuctuating coin price for a ﬁxed coin price with ﬂuctuating wallet balance. The net eﬀect is that the purchasing power of a Hayek Money wallet is just as volatile as a Bitcoin wallet balance."
My questions: Why is that? Why more brutal method - increasing or decreasing account balances pro-rata wouldn't work in light of R. Sam's argument? Why he says that purchasing power of such wallets (accounts) would be just as volatile as in pre-determined non-flexible money supply systems, like Bitcoin? Why we need shares as a catalyst, why we need them at all?
Or, maybe, we don't and increasing and decreasing accounts pro-rata is same effective?
Thanks for help.