Understanding the Voting Formula in Burn/Boost Game

The voting system that is used in Burn/Boost Game employs several mechanisms to ensure fairness and prevent manipulation. Here's a breakdown of the key components:

Sublinear Vote Impact

• To prevent large token holders from dominating the process, the vote power is not directly proportional to the tokens spent, but is calculated using the square root:

  $\text{Vote Power} = \sqrt{\text{Tokens Spent}}$

  This means that the impact of each token spent decreases as the amount increases.

Time Weighting Factor

• To discourage last-minute vote manipulation, a time weighting factor is applied. The earlier a vote is cast, the higher its weight. It is calculated as such:

  $w(t) = 1 - t$

  Where $t$$t$ the fraction of the elapsed time since the start of the voting stage (from 0 to 1).

Final Score Calculation

• The final score determines the outcome of the vote (Boosters win if positive, Burners win if negative). It is calculated using the formula:

  $\text{Final Score} = \sum_{\text{votes}} [\text{sign}(v_i) \cdot \sqrt{|v_i|} \cdot (1 - t_i)]$

  • Where:

    • $v_i$ - Tokens spent (positive for Boost, negative for Burn)

    • $t_i$ - Voting time (fraction of time elapsed from 0 to 1)

    • $sign(v_i) = +1$ for Boost, $-1$ for Burn