Decay Mechanism

The decay mechanism is integral to the Social AI platform's reward system, which promotes active engagement and discourages prolonged inactivity.

The decay process ensures that users remain active on the platform and continuously contribute to the community. When a user remains inactive for a certain period (7 days), their voting power decreases (10% every 7 days), reflecting a reduction in their influence over the distribution of rewards. This encourages users to stay engaged and participate regularly, fostering a vibrant and dynamic community.

The purpose of the decay process is twofold: First, it discourages users from accumulating voting power without active participation, ensuring that rewards are distributed to those who actively contribute to the platform. Second, it promotes a fair distribution of rewards by considering the current level of user activity and preventing a concentration of power among dormant accounts.

DECAY THRESHOLD DETERMINATION AND FAIRNESS

Determining the decay threshold involves setting a time frame after which a user's voting power begins to decay (7 days). The specific duration of the decay threshold is carefully considered to strike a balance between encouraging consistent activity and accommodating users who may have temporary interruptions, such as illness or other personal circumstances.

Fairness considerations play a crucial role in setting the decay threshold. The aim is to avoid penalizing users excessively for temporary inactivity while ensuring that prolonged inactivity diminishes their voting power. The decay threshold is set to achieve a fair and equitable reward distribution system by carefully analyzing user behavior, platform dynamics, and user feedback.

REDISTRIBUTION OF DECAYED POWER TO ACTIVE USERS

Decayed power no longer attributed to inactive accounts is redistributed to active users, further incentivizing their continued engagement. Note that any power reclaimed from the decay process is added back to the reward pool for distribution to active users. The redistribution process ensures that the reclaimed power is utilized to benefit users actively participating in the platform.

The redistribution of decayed power is conducted based on a predetermined algorithm, which considers the level of activity and contributions of active users. The algorithm calculates the share of decayed power that each active user should receive, proportional to their level of engagement and stake in the platform. This promotes a sense of fairness and rewards those who consistently contribute to the growth and vitality of the community.

The decay mechanism and the redistribution of decayed power help maintain an active and participatory user base on the Social AI platform. It encourages ongoing engagement, ensures fair rewards, and fosters a vibrant ecosystem where users are recognized and incentivized for their contributions.

Similarly, as stated previously, as users begin to engage again after their decay period has started, they receive 10% of their power back throughout each 7-day segment. If the user has been gone for 7 days, and their power is reduced by 10%, they would need to stay active for 7 more days to get that 10% back. When distributing power, the reward pool will determine the user's actual activity, their current decay rate, and such to allow users to reclaim their rewards over those 7 days.

For a more advanced statistical approach to reward calculation that encompasses content quality, user engagement, voting power, decay, and regeneration mechanisms, we will develop complex formulas integrating these factors. The approach will use statistical models to weigh each component dynamically and include visualizations to illustrate the behavior of these formulas.

To represent the described mechanisms mathematically and statistically, we can develop a set of advanced formulas that encapsulate the dynamics of power redistribution, decay, and regeneration within the Social AI Social platform. Let's break down the components:

Decay and Redistribution Mechanism

Decay Function D(t)

The Decay Function represents the decay of power over time for inactive accounts.

Where:

• (P0) is the initial power,

• (r) is the decay rate per time unit,

• (t) is the time elapsed since the last activity.

Regeneration Function R(t):

The Regeneration Fuction represents the regeneration of decayed power for users as they become active again.

Where (t) is measured in 7-day segments.

Redistribution Algorithm (A)

The Redistribution Algorithm determines the share of redistributed power each active user receives, based on their activity level and contributions.

Where:

• (au) is the activity score of user (u),

• (su) is the stake of user (u),

• (Preclaimed) is the total power reclaimed from decayed accounts,

• The sum in the denominator runs over all active users.

Advanced Statistical Model for Reward Calculation

To integrate content quality, user engagement, voting power, decay, and regeneration mechanisms, we can define a comprehensive reward function R(u,t) for user (u) at time (t):

Where:

• (Q(u, t)) is the quality score of user \(u\)'s content at time \(t\),

• (E(u, t)) is the engagement score of user \(u\) at time \(t\),

• (V(u, t)) is the voting power of user \(u\) at time \(t\),

• (ɑ, 𝛽, (𝛄)) are weights assigned to content quality, engagement, and voting power, respectively, reflecting their importance in reward calculation.

For the redistribution algorithm, given its complexity and dependence on multiple variables and user data, creating a single visual representation that encompasses all its dynamics might be challenging. Instead, consider plotting the effect of activity score and stake on a user's share of redistributed power for a given total reclaimed power.