Basis was something special. Its algorithm was such that if it ever stopped growing at a sufficient rate, it would explode to zero. And this would remain true no matter how much Basis had previously grown.
Every gain against a dollar by Basis was erased, either by paying off previous bets, or by paying “dividends”, and would not count for future price resiliency. If the market cap was 3 trillion and basis was used by 500 million people, and it needed to issue “bonds” to hold the peg, then the doom clock would start ticking again afresh.
In order for Basis to hold the price, you placed bets, not only that that the price would go back, but that the market cap would grow enough beyond a parity price to pay off every bet ahead of you in line. If the price just returned to parity, you still got nothing. So the more outstanding bets, the bigger the risk of placing a new bet. And this risk grew at a power ratio the farther behind the currency got.
“The critical insight is that as long as traders expect Basis price to correct [and grow] in the long-term...” which makes a prerequisite out of what they need to demonstrate.
And then there’s the part where they prove that their algorithm works by pretending that their currency behaves like USD does. Of course if your currency behaves like one of the most successful fiat currencies of all time, backed by the most powerful government in the world, then everything will be okay. If my hypothetical elderly Chihuahua dog had the driving ability and limbs of Micheal Schumacher in his prime, then my Chihuahua could turn in some nice lap times at the Nurburgring.
I think you're being unfair with your quotation there. The point they were making was that their system works over time, so whilst there can be temporary disjunctions on the long term the mechanism works, and therefore it's reasonable to expect parity to return which will help in the short term. If Basis were 95% of nominal value and you know that the algorithm ensures a return to 100% then actually you're incentivized to buy in, in the knowldge you can make profit lending liquidity. This may not be how it worked, but the idea that the predictable long term mechanism incentivizing short term behaviour isn't without merit.
Every gain against a dollar by Basis was erased, either by paying off previous bets, or by paying “dividends”, and would not count for future price resiliency. If the market cap was 3 trillion and basis was used by 500 million people, and it needed to issue “bonds” to hold the peg, then the doom clock would start ticking again afresh.
In order for Basis to hold the price, you placed bets, not only that that the price would go back, but that the market cap would grow enough beyond a parity price to pay off every bet ahead of you in line. If the price just returned to parity, you still got nothing. So the more outstanding bets, the bigger the risk of placing a new bet. And this risk grew at a power ratio the farther behind the currency got.
Basis could do nothing but explode.