Decentralization Ideal Votable Supply (DIVS) represents the votable supply required to maintain decentralization and safeguard the DAO from governance attacks at the current circulating supply level.
The goal of DIVS is to identify the optimal votable supply required to safeguard the DAO from potential hostile takeovers, assuming all existing governance safeguards are removed and the DAO operates in a fully decentralized manner. If the safeguards are eliminated to enable full decentralization, it is essential to determine the appropriate votable supply necessary to ensure the DAO's treasury protection.
Our research focused on the treasury that is subject to voting, as well as the factors influencing the cost of an attack & The formula for DIVS is defined as:
$$ DIVS = \frac{(200 - s)(100 - d)}{d \cdot t} \cdot T $$
Where:
Other than DIVS there are other factors the need some exposition such as the tokens required for an attack, denoted as Ta, depend on s. The relationship between Ta and the votable supply changes based on the source of acquisition:
$$ Ta = \frac{70}{(200 - s)} DIVS $$
The percentage of Ta sourced from outside the votable supply is determined by s, and we introduce a new variable Ts to represent this:
$$ Ta = \frac{s}{(100)} \cdot Ta $$
When the attacker acquires some part of the tokens outside of the available votable supply, for example, parts of the circulating supply that are not delegated to them, this causes a change in the votable supply. In this scenario, when s 0,
$$ F = DIVS + Ts $$
Where F is the final votable supply.
The time period for buying and selling tokens also influences the DIVS. We have calculated the amount of tokens an attacker can buy or sell with less than a 2% impact on the price, arriving at a value of 15 million. The following equation represents the number of days required for an attacker to acquire and sell tokens at s = 100. It can be found here.