Lately, Proof-of-Stake (PoS) consensus algorithms have been proposed as a replacement for Proof-of-Work (PoW). This prompts an interesting question: How many transaction validators should there be in a PoS blockchain?
The tradeoff is between trustworthiness and performance. Consider a PoS consensus algorithm offering Byzantine Fault Tolerance (BFT) properties. If the number of validators is high, the blockchain would be more trustworthy but offer lower throughputs. If the number of validators is low, the blockchain would be less trustworthy but would offer higher throughputs. This article proposes a market driven approach whereby the number of validators is determined by market dynamics.
Two Native Assets Types
Our blockchain has two native asset types; a liquid asset type and an illiquid asset type. Let’s call the illiquid one BondCoin and the liquid one CashCoin. The blockchain has relatively small number of total coins; lets label this number maxCoins. Each coin is represented by a public-private key pair.
- To start with, a PoW consensus algorithm only mints BondCoins.
- After all the BondCoins have been minted, the PoW algorithm subsides and PoS takes over. Owners of BondCoins are the validators.
- The private-key of a BondCoin can be used to cast votes during the various phases of the BFT PoS consensus protocol. We can assume the BLS signature aggregation scheme as proposed in the ByzCoin paper for aggregating signatures of BondCoins.
- Each BondCoin is of unit denomination and cannot be divided into smaller values.
- There is a maturity duration d associated with each BondCoin, say a month. After d time, a BondCoin gets automatically converted into a CashCoin. As an important side benefit, the maturity duration helps in disabling voting rights of dormant BondCoins.
- The owner of each BondCoin can also convert it to a CashCoin before maturity but there is a penalty p associated with such a transaction. The convertor derives a value of [CashCoin - p] and p is distributed as fees to other validators.
- BondCoins accrue transaction fees for participating in the consensus process. The fees collected during each block are equally distributed among the BondCoins.
- BondCoins collectively determine, via consensus, the amount of fees to be charged for processing transactions. This is a key point. We will soon see that for any given number of BondCoins in the system, there is an equilibrium value for the fee amount to which it settles. Transaction validators can also force the fee value to a certain level in order to increase or decrease the number of validators in the system.
- CashCoins can exist in any denominations and hence are very liquid. You can buy coffee with CashCoin.
- Fractions of CashCoin can be accumulated into a unit of CashCoin and further converted into a unit of BondCoin by the owner.
Sources of Demand for CashCoins and BondCoins
What we have created with the dual asset types concept is a wonderful interplay between the demand for CashCoins, the demand for BondCoins and the transaction fees. This is very similar to the interplay between the demand for cash, the demand for bonds and the central bank determined interest rate. You can read an excellent description here.
Lets understand the interplay between CashCoins, BondCoins and transaction fees better by noting the costs and benefits of holding either.
Benefits of holding CashCoins
- Transactions: People will hold CashCoins to buy goods and services.
- Precautions: People will hold CashCoins for contingencies like medical emergencies or the sudden loss in value of a national currency.
- Speculation: Speculators that believe that the BondCoin prices are too high can sell them and hold CashCoins instead guarding against possible drops in value of BondCoin.
In short, the advantage of CashCoin is that it is highly liquid.
Cost of holding CashCoins
- The price of holding CashCoins is the transaction fees.
Benefits of holding BondCoins
- Storage: Risk free time shifting of value.
- Earn Fees: Holders of BondCoin earn a fraction of the transaction fees.
- Speculation: BondCoin prices will fluctuate constantly. Speculators that believe that the BondCoin prices are low can buy them.
Cost of holding BondCoins
- Loss of liquidity
Demand Curve for CashCoins
The various sources of demand for CashCoins (transactions, precautionary and speculative) will vary negatively with transaction fees. An additional source of demand for CashCoins is from participants wanting lesser decentralization, faster throughputs and lower fees. Let’s label this demand as the higher network performance demand. Lower the fees, higher the demand for CashCoins.
Lets suppose CC** is the total amount of CashCoins at some point in time. I.e., CC** is the supply of CashCoins. Then, the CashCoin market equilibrium will occur at transaction fee f** where the demand meets supply. Now, suppose CashCoin availability increases to CC*, the market equilibrium will occur at transaction fee f* where the demand curve meets the new supply.
Change in Demand for CashCoins
Previously, we have identified 4 sources of demands for CashCoins. i) transactions demand, ii) precautionary demand, iii) speculative demand and iv) higher network performance demand. The various sources of demand for CashCoins can change. For example, during festivals in light of higher retail spending, the transaction demand may rise moving the demand curve as shown in the above figure.
Demand Curve for BondCoins
The various sources of demand for BondCoins (storage, fees and speculative) will vary positively with transaction fees. An additional source of demand for BondCoins is from participants wanting more decentralization and who do not mind paying higher fees. Let’s label this demand as the higher decentralization demand. Higher the fees, higher the demand for BondCoins.
Lets suppose BC* is the total number of BondCoins at some point in time. I.e., BC* is the supply of BondCoins. Then, the BondCoin market equilibrium will occur at transaction fee f* where the demand meets supply. Now, suppose BondCoin availability increases to BC**, the market equilibrium will occur at transaction fee f** where the demand curve meets the new supply.
Change in Demand for BondCoins
Previously, we have identified 4 sources of demands for BondCoins. i) storage demand, ii) fees demand, iii) speculative demand and iv) higher decentralization demand. The various sources of demand for BondCoins can change. For example, if the transaction fees increase in anticipation of subdued transaction volumes, the fee demand may rise moving the demand curve as shown in the above figure.
The Common Market Equilibrium
The supply of BondCoins is simply maxCoins - supply of CashCoins. As shown below, it can be represented by a single line. The supply curve intersects with the demand curves of CashCoin and BondCoin at the same point. This is the common market equilibrium for both CashCoins and BondCoins. There is of course a single fee value f for this common market equilibrium.
This common market equilibrium represents the steady state of the system that respects the aggregate demands and supplies for CashCoin and BondCoin. The number of BondCoins at this equilibrium represent the number of validators in the blockchain.
- There are 4 sources of demands for CashCoins: i) transactions demand, ii) precautionary demand, iii) speculative demand and iv) higher network performance demand.
- There are 4 sources of demands for BondCoins: i) storage demand, ii) fees demand, iii) speculative demand and iv) higher decentralization demand.
- The higher the transaction fees, the lower the aggregate demand for CashCoins and higher the aggregate demand for BondCoins. Conversely, the lower the transaction fees, the higher the aggregate demand for CashCoins and lower the aggregate demand for BondCoins.
- The demand for CashCoins and BondCoins will change over time.
- The total number of coins (number of CashCoins + number of BondCoins) is a constant. The supply curve of CashCoins (and also BondCoins) is a vertical line.
- CashCoin market equilibrium occurs where the quantity of CashCoin demanded meets supply for CashCoins. Similarly, BondCoin market equilibrium occurs where the quantity of BondCoins demanded meets supply for BondCoin.
- There is a common market equilibrium for both CashCoins and BondCoins. There is a single fee value for this common market equilibrium.
- The number of BondCoins at the common market equilibrium represent the number of validators in the blockchain. We conclude that market forces can determine the number of validators for the dual asset types PoS blockchain.