Staking Mechanism and Voting Power

Staking is a fundamental feature of the Social AI platform that allows users to lock up their tokens and participate in the governance of the ecosystem. Users gain additional benefits and voting power within the platform. The staking mechanism operates as follows:

STAKING TOKENS

Users can stake their tokens, locking them in a designated smart contract. Staked tokens cannot be transferred or traded during the staking period. Users demonstrate their commitment to the platform by staking and gaining various advantages.

VOTING POWER

Staked tokens contribute to a user's voting power, determining their influence and decision-making authority in platform governance. The more tokens a user stakes, the higher their voting power and ability to participate in voting events and proposals.

GOVERNANCE PROPOSALS

The Social AI Social platform enables users to engage in governance by actively submitting and voting on proposals. These proposals can involve platform updates, feature enhancements, rule changes, or other important decisions affecting the ecosystem. The voting power of staked tokens determines the weight of a user's vote on each proposal.

VOTING PROCESS

When a governance proposal is submitted, staked token holders are notified and allowed to cast their votes. Each staked token represents one vote. The voting process is designed to be transparent and secure, utilizing blockchain technology to ensure the integrity and immutability of the voting results.

VOTING RESULTS

The outcome of a governance vote is determined by the majority of votes cast. The proposal with the highest number of votes, weighted by voting power, will be implemented if it meets the predefined acceptance criteria. This ensures that the platform's governance decisions align with the community's collective interests.

STAKING MECHANISM AND VOTING POWER FORMULAS

Staking Tokens to Voting Power Conversion:Voting Power Calculation:

• Let Si be the amount of tokens staked by user i.

• Let T be the total amount of tokens staked by all users.

The voting power (Vi) for user (i) can be calculated using a logarithmic function to diminish the marginal voting power increase from staking additional tokens, enhancing fairness:

Governance Proposals Evaluation: Proposal Support Threshold:

• Let (Pvotes) represent the number of positive votes on a proposal.

• Let (Nvotes) represent the number of negative votes.

A proposal's success threshold could incorporate the Gini coefficient (G) to account for voting power inequality:

Where (𝝺) is a function adjusting the threshold based on the Gini coefficient, making it harder for proposals to pass in highly unequal voting power distributions.

Voting Power Decay and Regeneration: Voting Power Decay Over Time for Inactivity

• Let (D) be the decay factor per unit of time (e.g., days).

• Let (t) be the time of inactivity.

The decayed voting power (Vi, decayed) can be modeled as an exponential decay function:

Voting Power Decay and Regeneration: Regeneration of Voting Power

• Let (R) be the regeneration rate per unit of time.

The regenerated voting power after returning to activity:

Where (tactive) is the time since becoming active again.

Weighted Voting for Governance Proposals: Weighted Voting Calculation

• Incorporate a weighted voting system where each vote is weighted by the voter's voting power.

The weighted vote (WV) for a proposal is:

Where (Votei) is the vote cast by user (i), and (Vi, adjusted) is the adjusted voting power considering decay/regeneration.