PS Formula for all Edge Cases

From the previous Edge Cases we can extend the general formula to cover for those cases:

$PS_{\tiny n} = \begin{cases} PS_{\tiny(n-1)} &\text{if } TCM = 1 \\ PS_{\tiny(n-1)} \cdot p_{\tiny \ominus} &\text{if } GC = 0 \\ min(PS_{\tiny(n-1)} \cdot \Delta \overrightarrow P, PS_{\tiny(n-1)} \cdot c) &\text{if } \Delta \overrightarrow P \ge 100 \\ max(PS_{\tiny(n-1)} \cdot \Delta \overrightarrow P, PS_{\tiny(n-1)} \cdot p_{\tiny \ominus}) &\text{if } \Delta \overrightarrow P < 100 \end{cases}$

Scenarios:

• Case A: Addresses a Member who's $GC = TCP$ (see Cannibal Member).

• Case B: Applies if a Member was inactive during an entire period.

• Case C: Applies if a Member is performing better than the previous period ( $\rightarrow \overrightarrow P_{\tiny n} \ge \overrightarrow P_{(\tiny n-1)}$). By using c, the constraining factor, it ensures that PS cannot spike more than 40% higher from a period to the next.

• Case D: Applies if a Member is underperforming respect to the previous period ( $\rightarrow \overrightarrow P_{\tiny n} < P_{(\tiny n-1)}$). By using $p_{\tiny \ominus}$, the penalty factor, with $p_{\tiny \ominus} = 0.4$, it ensures that PS cannot drop more than 40% lower from a period to the next.

These scenarios cover the vast majority of cases. Either way, soon after the V1 release, we’ll be adding additional coverage for edge-cases such as imprecise assignation of weights to internal community tasks.