Our Solution: Weighted Reward Formula

Our Solution: Weighted Reward Formula

To address these issues, we’ve created a formula that balances both the quantity of messages and the quality of contributions, while factoring in the size of the group. This way, even smaller groups with fewer messages can compete fairly for rewards.

Reward Formula

We propose the following formula to fairly distribute tokens across groups of different sizes and activity levels:

$R=T×\frac{(∑_{i=1}^nM_i×Q_i)^{0.5}}{U^{0.5}}$

Where:

• ( $R$ ) = Total reward for the group.

• ( $T$ ) = Fixed amount of tokens to be distributed every 24 hours.

• ( $M_i$) = The score for each message ( i ), based on quality (usefulness, engagement, relevance).

• ( $Q_i$) = The engagement score of each message ( i ), measuring interaction (likes, replies, etc.).

• ( $U$ ) = Total number of active users in the group.

• ( $n$ ) = Number of messages in the group during the 24-hour period.

Explanation

• Message Score & Engagement Weighting:

  Each message is assigned a score based on its quality and engagement. The message quality score ( $M_i$ ) reflects how useful or relevant the message is, while the engagement score ( $Q_i$ ) accounts for the interactions (likes, replies, etc.). These two factors are multiplied to calculate the overall score for each message. $M_i ​ ×Q_i ​$

  This ensures that both the quality of the message and the engagement it generates contribute to the reward.

• Square Root Weighting for Message Score:

  To ensure fairness between larger and smaller groups, we apply a square root to the total message score. This prevents large groups with high message volumes from overwhelming the reward system, while still allowing smaller groups with fewer but high-quality messages to compete effectively.

  $(∑_{i=1}^nM_i×Q_i)^{0.5}$

  By taking the square root of the summed message scores, we reduce the impact of message quantity, giving more weight to the quality and engagement of each message.

• Square Root Weighting for User Base:

  Similarly, we apply a square root to the number of active users in the group. This adjustment ensures that large groups don’t automatically get more rewards just because they have more participants. It levels the playing field, giving smaller groups a fairer chance.

  $U^{0.5}$

  The square root of the user base balances the impact of group size on the reward distribution.

By applying these adjustments, we ensure that both message quality and group size are fairly considered, making it possible for smaller, highly engaged groups to earn rewards at a level that competes with larger groups.