Example

Example

Let’s say two groups, Group A and Group B, are participating:

• Group A:

  • 5 active users

  • 10 high-quality messages with strong engagement

  • Total ( $M^Q$ ) score = 1000

• Group B:

  • 50 active users

  • 100 messages with moderate engagement

  • Total ( $M^Q$ ) score = 3000

Using our formula:

For Group A:

$R _A ​ =T× \frac{(1000)^{0.5}}{(5)^{0.5}} =T×14.11$

For Group B:

$R _B ​ =T× \frac{(3000)^{0.5}}{(50)^{0.5}} =T×7.74$

Even though Group B has more messages and users, the formula ensures that Group A still gets a significant reward because of the quality and engagement of their content.

Conclusion

This formula offers a balanced and fair way to distribute tokens, ensuring that both large and small groups are rewarded based on meaningful contributions rather than just sheer numbers. By adjusting for both message quality and group size, we can create an ecosystem where everyone has a fair chance to earn rewards, while still promoting valuable, engaged discussions.