🖥️Voting Power

Calculating voting weight and voting power

The stake weighting function is based on a quadratic formula, using the amount and duration of FISH tokens staked.

Let $m$ be the maximum staking period (1092 days) , $x$ be the number of days passed since the beginning of the period, and $V$be the maximum voting weight (currently 9). The voting weight at a given time $x$ can be described as:

$$f(x)=V∗(m^2−x^2)/m^2+1$$

$+1$ is added in the end to shift the weights to lie in $[1,V+1]$instead of $[0,V]$.

Users will usually not stake the maximum duration, so $x$ has to be computed based on the remaining days until unstaking:

$$x=m−RemainingDays$$

The user’s voting power $VP$ at a given time $x$ is the product of their stake $x$ and their voting weight:

$$VP(x)=f(x)∗s$$

The total voting power equals the sum of the voting power of all users. However, since we can’t iterate over an array with unlimited size, we need to compute it differently. Instead of summing up the user voting powers, we introduce a mapping, which stores the total amount of FISH to be unstaked on a given day, and call it stakedUntil.

Whenever a user stakes FISH, not only is their staking balance updated, but also stakedUntil[unstakingDay]. Whenever a user increases their staking balance, the mapping also needs to be increased. Whenever a user increases their staking time, their stake is subtracted from stakedUntil[previousUnstakingDay] and added to stakedUntil[newUnstakingDay].

Now, we can compute the voting power of all FISH staked until a given point in time in a single operation. The daily voting power $DVP$ is given by:

$$DVP(x)=f(x)∗\textstyle\sum_{u}s_u(x)$$

where $\textstyle\sum_{u}s_u(x)$ is the content of stakedUntil[x].

The total voting power can then be computed by summing up the daily voting powers of the next $m$ days:

$$TVP=\textstyle\sum_{x=0}^ m∗DVP(x)$$

This process requires $m$ iterations. With a maximum staking duration of 3 years, this would cost approximately 1,000,000 gas. In order to save gas costs, we decided to stake in bi-weekly periods instead. As a consequence, voting weights are only adjusted every 2 weeks and we need a maximum of 78 iterations (instead of 1095).

The stakedUntil mapping needs to be checkpointed to allow the computation of the total voting power for a point of time in the past. The same is true for the user stakes.

Delegating Voting Power

Given the possibility of delegation, a user can have a potentially large number of addresses delegating voting power to their address, with each of these other addresses staking for different durations. The voting power of a delegatee is computed the same way the total voting power is computed: as a sum of the voting powers per unstaking day.