Governance tokens are an asset class that form a large part of decentralised finance. Governance in these distributed, open-source networks is a frequent point of discussion in the crypto community and is a core component of decentralisation. Their utility is often based on incomplete governance theories or as a representation of speculation for the protocol they represent. The token is not directly indicative of the protocol use or performance and its use in governance is still nascent. These innovative networks allow the testing of intricate governance models not possible in traditional business and finance. Despite their development being far from complete, it’s useful to measure the value of these tokens as their underlying protocols accrue more users and more liquidity. For an investor, it is also necessary to have some sort of framework when valuing tokens for reporting that represent governance in a project that has yet to launch. This begs the question; “is there a way to accurately value a governance token?”

Most people have a vague idea of what governance in any system entails, but to avoid ambiguity; Governance encompasses the process by which a system or organisation is controlled and operates, and the mechanisms by which it, and its people, are held to account. Ethics, risk management, compliance and administration are all elements of governance. Democracy, a form of governance that means “rule by the people”, is the foundation of modern western society. The term was coined by the skilled orator and politician Pericles of ancient Athens to describe their city state’s system of rule, which reached its golden age in 430 B.C. Most likely, Athenians were not the first to adopt a democratic styled system (Places in India have traditions of democracy that claim earlier origins), however due to the Greeks naming it, they have a good claim at being the “first” democracy. Before democracy, authoritarian systems were accepted as the best and most efficient systems of rule. Governance was most commonly dictated by a powerful individual or family, their claim to power often supported by belief systems and religion. Similar to democracy redistributing power of governance from a single monarch to officials elected by the people, governance tokens in DeFi protocols aim to redistribute authoritarian governance of legacy financial systems to the individuals participating in those systems. In turn, governance tokens empower users by actively engaging them in the direction and growth of a protocol.

The Price of Open Source

The decentralised finance protocols that exist today often have governance tokens that allow the users of the protocol to dictate its future. There are several things to consider when examining the price given to a governance token. The governance tokens allow the owner to vote for changes to the network in which they belong, normally in proportion to how many tokens they own. This allows anyone the opportunity to own these tokens and participate in governance.

Being open source, the networks governed by these tokens also present an opportunity to the minority to fork the code and create a network that suits them. In a system that can be copied, what is the value of this voting power? If the entirety of Facebook could be copied, shareholders may care less about voting rights. Consequently, the maximum price a network participant will pay for 51% (voting majority) is bound by the cost of a network fork. Cost is equal to the difference between the net present value of the pre-fork and post-fork business. Unfortunately, this is impossible to predict accurately, however there are some key measurables that assist in estimating this value.

Let’s look at an example. Koji has recently invested in a company called Thales that uses 0x to provide an orderbook binary options trading platform. For Thales, the future of 0x is important as their business relies on this platform and so they would be interested in having some governance power. They could trust that the community will maintain a suitable series of developments for the 0x protocol and if they strongly disagreed with a change to the platform, they could fork the 0x code and create their own network. Alternatively, if they wanted to secure the future of 0x without forking they would need to purchase 51% of the voting power.

Let’s say Thales reaches a net present value of $360.6 million and they have decided not to purchase majority voting power. The 0x community votes on a decision that compromises Thales’ platform, so the Thales team decide to fork the code and create their own version of 0x.

Let’s assume a 30% decrease in revenue due to reputation damage and lower volume (no shared liquidity pool). They also must hire 10 new engineers to maintain the new 0x network, their growth rate declines due to absence of liquidity and reputation, and their marketing costs increase to account for this reputation damage. Due to increase costs and a 30% decrease in revenue, Thales now has a net present value of $105.8 million.

Forking is nontrivial and is generally avoided. Yet if there is a compelling reason to upgrade or a major disagreement in the user base, a fork can occur and with it, pull some of the network value away. Therefore, the network value of a governance token is fundamentally constrained by this net cost of forking the network. Code is only one aspect of a successful network along with platform, company, and community; however, it is a foundational aspect of a connected DeFi network.

This means that logically, Thales would be willing to pay up to $254.8 million for voting majority of the 0x platform (disregarding risks of another group forking the code). It is extremely rare and not ideal for a DeFi protocol to have an entity with voting majority (as it destroys the ‘decentralised’ in decentralised finance), however this provides a value cap on voting majority depending on the protocol.

Shapley Values

For a new protocol that has recently become public, the newly available governance tokens undergo price discovery whilst trading on exchanges or in a genesis event like a gnosis auction, however due to the nature of voting power, not every token is of equal value at any one time. Hypothetically, if a single entity (or multiple smaller entities in collusion) owned 50% or more of the governance tokens, it wouldn’t matter what any other tokens voted for as they would be overridden by this significant token holder. Therefore, as the proportion of tokens held by the significant shareholder approaches 50%, the remaining governance token values theoretically approach 0. This can be quantified by the Shapley values.

The Shapley value is a solution concept in cooperative game theory. It was named in honour of Lloyd Shapley, who introduced it in 1951 and won the Nobel Prize in Economics for it in 2012. In essence, Shapley value describes the relative voting power of a share in the presence of large or significant shareholders. The Shapley value of a small “oceanic” shareholder depends on the holdings of significant shareholders. If a firm has *n *outstanding shares, one significant shareholder holding a fraction *x *of the shares and many oceanic shareholders, the significant shareholder’s Shapley value is {x/(1-x) for *x *< 0.5; and 1 for x ≥ 0.5}. The oceanic shareholders have combined Shapley values of {1 — (the significant shareholder’s value)}, and thus Shapley value per share of {(1–2x)/n(1-x)2 for *x *< 0.5; and 0 for *x *≥ 0.5}. The per-share Shapley value of oceanic shareholders, and thus the market value of their votes, approaches zero as the significant shareholder approaches absolute control (*x *= 0.5), and disappears once control is achieved.

Therefore, a reasonable way of valuing a governance token would be to determine the distribution of tokens (using Dune etc), then calculate the Shapley values of the oceanic and significant shareholders. From this, you could then use the above formula to get a relative value for n tokens. Using the market cap or current valuation of the company, you can then calculate a valuation estimate for each token.

Example: Uni Governance token

The Uni token has a supply of 519,857,388 and a market cap of $8,803,298,450. Currently, there is a single wallet that owns 12.9% of supply; this is the significant wallet. Therefore we can calculate the significant token holders relative voting value with: 0.129/(1–0.129) = 0.148 or 14.8%. The per share/ token value considering this significant shareholder can then be calculated with:

(1–0.258)/519,857,388(1–0.129)2 = 1.88141 e-9 %

We can multiply this percentage by the market cap to get the relative value in USD of a single token:

1.88141 e-9 x 8,803,298,450 = $16.56

• Note this is the relative value of a single share or token. If more than one token is owned the value of both tokens increases etc.

Quadratic Voting

Incorporating Shapley values is an effective method for quantifying the relative value of the governance power of each token in a traditional model. However, projects are starting to implement complex systems of government such as quadratic voting in the aim of further democratising defi governance systems. The quadratic voting formula is: Cost to the voter = (Number of votes)2. So, while you are increasing the chances of victory for your issue with each additional vote, the quadratic nature of the voting ensures that only those who care deeply about issues will cast additional votes for them.

Although quadratic voting can be more complex than traditional voting mechanisms, it better protects the interests of small groups of voters that care deeply about particular issues. By increasing the cost of each additional vote, it disincentivises voters that don’t care about issues from casting several votes for them. It also allows voters to show the intensity of their support for a given issue by casting several votes for it — at the expense of their ability to vote on other issues.

Quadratic voting more accurately represents the ‘oceanic’ shareholder in a governance model, however in DeFi its effectiveness is limited due to the ability of an individual to create multiple wallets. This enables an individual to spread their governance tokens across wallets and potentially circumvent some of the quadratic voting mechanism. Without a ‘know your customer’ (KYC) system in a DeFi protocol, this would be impossible to protect against.

Commitment Voting

One potential solution to quadratic voting’s reliance on stable fixed identities and collusion detection is commitment voting. Commitment voting does not reserve voting power exclusively for wealth over preference intensity, superior information, or long-term strategic thinking like one token one vote systems (1T1V), yet it also solves some of the issues quadratic voting has in the DeFi ecosystem. Commitment voting is a version of time weighted voting that has 3 main features:

1. The influence of a vote is determined by the product of both the token quantity and the amount of time a voter is willing to lock up those tokens:

Vote weight = token quantity * staking lockup period

2. Tokens are only subject to the lockup if they vote for the winning proposal, the votes for the losing side are released from lockup at election conclusion.

3. Lockup is cumulative in proportion to proposals voted and won. This way, if two proposals are voted on and won then lockup period is calculated as:

Total lockup period = staking lockup periodelection a + staking periodelection b

Good governance is not determined by all token holders voting, rather by the token holders voting well. By having a consequence to voting, the token holders are forced to demonstrate a level of conviction if they wish their vote to be registered. This reduces the effect of rational ignorance present in traditional voting. Commitment voting also harnesses socially desirable political competition that results in encouraging voters to increasingly invest in the outcome (in contrast to traditional politics, where to gain votes, electees promise additional spending).

Oligopoly is still present to an extent in commitment voting, however, it is drastically mitigated via the commitment required for each winning vote. Smaller voters can group together and outvote a significant token holder if they choose to stake their tokens for longer. The more confident a token holder is in the token/protocol it represents, the more influence they can have in governance by staking for longer. This will incentivise informed voting.

Developing Governance

In Vitalik’s recent article titled, “Moving beyond coin voting governance”, he explores some of the limitations of current DeFi governance systems and proposes some potential future implementations to further secure the voting integrity of decentralised systems. In addition to the vulnerability to attackers ‘vote buying’, he highlights 3 limitations to current voting systems; small groups of large token holders are better at successfully executing decisions than large groups of small token holders, coin voting governance empowers coin holders and their interests at the expense of other parts of the community, and conflicts of interest in token holders of multiple protocols. Although the most serious of these vulnerabilities have yet to be majorly exploited, as the networks grow and communities expand, these limitations will come to the forefront. Vitalik proposes several potential solutions that implement futarchy systems and reputation, anything that can delineate from a simple system of token amount=voting power.

Introduced by Robin Hanson in the early 2000s, futarchy votes essentially become bets. Votes that are cast for the results that lead to a net positive outcome for the institution are rewarded and votes cast for a net negative outcome are disincentivised. Voters who research thoroughly and vote correctly, eventually amass more tokens/

shares over time and eventually have more voting power. This incentivises informed and active voting.

This model has been traditionally difficult to implement, as objective functions are very difficult to define and require a control state to refer to. It almost requires a multivariate analysis of the two possible realities to objectively define what is net positive and negative over a period of time (price improvement is not the sole measure of success). In DeFi, votes can lead to a fork of the network that present a scenario that closely model parallel realities. Therefore, incorporating this futarchy system in a hybrid voting model could be successful in decentralised governance scenarios. These improvements are yet to be made, however complex solutions such as these will most likely be experimented with in DeFi soon.

Conclusion

To value these governance tokens that employ alternate forms of voting mechanisms, some small edits to the Shapley value formula must be made. For quadratic voting, the root of the relative proportion of supply must be implemented. The new formula to determine isolated proportion of voting power that incorporates quadratic voting for one token is:

(1-sqrt(0.258))/519,857,388(1-sqrt(0.129))2

For commitment voting, an extra variable must be added for the lockup commitment: Xtime. The formula to value isolated tokens therefore becomes:

(1–0.258)/519,857,388(1–0.129)2 * Xtime

The potential of governance, especially in the DAO model is still in its infancy. Just like any foundation shaking changes to a traditional, powerful system, governance in DeFi utilising tokens will take many years to perfect and it will face resistance from the systems it is attempting to replace. Education about the technicalities of how this new system will work, as well the implications it will have on our current methods of governance is essential to accelerate its acceptance. Decentralised governance extends further than finance as it is attempting to more accurately represent the opinions, beliefs and contributions of individuals to the systems in which they participate and represent. This can be seen with the success of DAOs that are operational today.

References

· https://www.governanceinstitute.com.au/resources/what-is-governance/

· https://hackernoon.com/a-framework-for-valuing-governance-tokens-0x-49d2cf2ef5bc

· https://www.history.com/news/what-is-the-worlds-oldest-democracy

· https://towardsdatascience.com/what-is-quadratic-voting-4f81805d5a06

· Berg, Davidson and Potts, RMIT. 2020. Commitment voting: a mechanism for intensity of preference revelation and long-term commitment in blockchain governance