New Research Reveals That Proof-of-Stake Governance Tends to Maintain Cryptocurrencies’ Level of Decentralization in the Long Run

• It has been presumed that the “Proof-of-Stake” governance protocol used in blockchains would eventually generate extreme centralization, thus negatively impacting cryptocurrencies.
• A new paper published by professors Ioanid Rosu from HEC Paris and Fahad Saleh from Wake Forest University shows otherwise. Proof-of-Stake governance tends to maintain cryptocurrencies’ level of decentralization in the long run. 
• The research has important consequences for investors and the long-term sustainability of cryptocurrencies.

On January 1, 2020, 1 US dollar was worth approximately 7,000 bitcoin. Fast forward a year and that number has almost multiplied by 6 to an average of over 40,000. Research on cryptocurrencies has raised several concerns regarding its long-run viability. Those concerns have led to various proposals for new blockchains that seek to generate decentralization while avoiding its various documented limitations.

New research by HEC Paris professor Ioanid Rosu and Wake Forest University professor Fahad Saleh highlights how, contrary to what is presumed, “Proof-of-Stake governance” tends to maintain cryptocurrencies’ level of decentralization in the long run.

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Background

A cryptocurrency (a type of electronic money) is a transaction log based on a distributed ledger technology such as blockchain. A consensus mechanism is used in computer and blockchain systems to achieve the necessary agreement on a single data value or a single state of the network among distributed processes or multi-agent systems.

Several protocols for achieving blockchain consensus exist, the most important being Proof-of-Work (PoW) and Proof-of-Stake (PoS).

The PoW protocol requires agents to compete to update the blockchain by solving a computational puzzle. With PoS, the blockchain is updated by a randomly selected stakeholder, where the probability of an investor being drawn is equal to the investor’s share, i.e., the fraction of the points that the investor owns. PoS specifies the criterion for updating the blockchain as a simple lottery. The blockchain possesses a native asset, called a cryptocurrency, which is both created and settled on the blockchain. At each relevant time, PoS randomly and uniformly selects among each unit of this cryptocurrency and then grants the updating authority to the owner of the selected unit.

The implication is that the ability to update the blockchain is proportional to one’s holding of the cryptocurrency. For example, holding 1% of the cryptocurrency yields an individual a 1% chance of providing the next update. New lotteries are conducted regularly so that the winner of one particular lottery does not gain centralized control of the blockchain.  Nonetheless, the winner of the lottery not only earns the right to update the blockchain but usually receives also a “block reward” of coins in the same cryptocurrency.  The coin reward increases the chance of repeated lottery wins, thus generating a “snow-ball effect” among coin owners.  Thus, the conventional wisdom holds that the PoS coin reward structure would cause only a few individuals to eventually win all the lotteries.

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Key finding

Rosu and Saleh used a discrete-time infinite-horizon model to analyze several investors who can trade a risky cryptocurrency with units called coins. The professors’ paper shows that PoS, in fact, tends to maintain its level of decentralization in the long run, defying the conventional wisdom that it would lead to centralization.

Rosu and Saleh note the example of a cryptocurrency with only two coins, one held by Alice and one held by Bob, and with a potential reward of one coin for each lottery winner. The conventional wisdom worries that Alice begins with a 50% probability of winning the first lottery, but winning that lottery escalates Alice’s subsequent win probability to approximately 67% and further wins only increase that probability until Alice is almost certain to always win. Rosu and Saleh’s first key result shows that this intuition is flawed: Just as there is a chance that Alice has a streak of victories moving her close to a 100% holding of coins, there is an equally likely probability that Alice has a streak of equally long losses leading her close to a 0% holding of coins. For example, two wins in a row would increase her coin share to 75% and two losses in a row would decrease her coin share to 25%.  After two wins in a row, Alice’s winning chance in the next lottery is 75%, in which case her share will further increase to 80%, but if she loses (with 25% probability), her share will decrease to 50%.

Rosu and Saleh note that in the scenario in which Alice starts as “rich” (with 75% share), she does have a large chance (75%) of getting even richer (with 80% share) but the increase in share in this lucky scenario is small (5%).  Nonetheless, there is a chance (25%) that she does not win the lottery, in which case her 15% share loss (from 75% to 50%) is much larger than the 5% increase in the lucky scenario. More generally, the potential for increase in an individual’s coin share is offset by the potential decrease in that individual’s coin share. Formally, Rosu and Saleh establish that each owner’s coin share is a “martingale” or a “fair game”, as it is often called in the probability research.

Another key result by Rosu and Saleh is that trading in a PoS cryptocurrency does not provide incentives for investors to amass coins to increase the probability of earning even more coins in the future.  A purchase of coins does increase the probability that an investor wins a subsequent lottery.  However, the coins owned also face dilution, as all outstanding coins decline in value once the block reward from the lottery inflates the supply of existing coins. Rosu and Saleh prove that in equilibrium the dilution effect exactly offsets the probability increase, which implies that investors have no incentive to amass large cryptocurrency holdings via trading.

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