Hop offers its users the opportunity to exchange units of USD value and bitcion value on a decentralized trustless platform.
Hopdollars and Hopbits sound more like units which have the price of USD and price of bitcoin written on them. Having the price written on it is not what gives it value. What will give them value is the ability to exchange these units for "real" USD, or actual BTC. How will someone exchange hopbits for bitcoins and hopdollars for dollars? Otherwise you would just have a decentralized ledger where people are trading hopbits for hopdollars (but never actual BTC or redeemable USD).
If I understand it correctly this is what he's claiming:
The value of Hopbits and Hopdollars should theoretically be very close to the value of Bitcoins and USD. Hopbits and Hopdollars actual values would be determined by external exchanges. The system attempts to alter the value of Hopbits and Hopdollars by increasing or decreasing the amount of "Hops" backing Hopbits and Hopdollars. These increases and decreases in backing are driven by PoS miners who vote up/down depending on the market price of Hopdollars and Hopbits on external exchanges. I.e. PoS miners would scrape exchange sites or use exchange APIs to determine their votes, and it's in the best interest of PoS miners to vote in a way that would make the prices on the exchanges to tend toward the value of Bitcoins and USD.
Is the author still advocating this idea? There's not much rationale for the design decision presented in the document. Without rationale and analysis, the equations defining the dynamics of the system look arbitrary to me.