# PS Simulations

### Tests & Simulations - trust but verify

#### 1. Stress factors [*TCM* + *iCL*]

*TCM*+

*iCL*]

**Total Community Members (TCM) spike & drop**The simulation includes periods with different numbers of community members, ranging from 1 to 100,000.

**iCL random fluctuations**Fluctuating $\overline{iCL}$: The average individual Commitment Level varies across periods to simulate changes in overall community commitment.

Changing $iCL$: Each member ($M_{\tiny [1, 2, 3]}$) has a different individual commitment level, that keeps changing and being updated each period.

#### 2. Fixed Parameters

10 periods

3 individual members ( $M_{\tiny [1]}, M_{\tiny[ 2]}, M_{\tiny [3]}$ )

a stable performance ( $\overrightarrow P = \frac {GCp}{ECp}$ ) set to a constant value of 1.05 (105%).

#### 3. Parameters used

*TCM*(Total Community Members): The number of members in the community for each period.$\overline{iCL}$ (Average Individual Commitment Level): The average commitment level of all members in the community for each period.

${iCL}$ (Individual Commitment Level): The commitment level of each member, ranging from 1 to 10.

$fiCL$ (Fractional Commitment Level): The fraction of the total commitment level attributed to each member.

*TCP*(Total Contribution Points): The total number of contribution points available in the community for each period.*ECp*(Expected Contribution Points): The expected number of contribution points for each member based on their*fiCL*, calculated as $ECp = fiCL \cdot TCp$.*GCp*(Given Contribution Points): The actual number of contribution points contributed by each member, calculated as $GC = \overrightarrow P \cdot EC$.*PS*(Participation Score): The cumulative participation score for each member, calculated as $PS_n = PS_{n-1} \cdot \overrightarrow P$, with $PS_{\tiny 0} = 100$.

#### 4. Approximations for convenience

*TCP*: The total contribution points available in each period. Here we constrained using the formula $TCP \le TCM \cdot 100$ "*heavy tasks*” worth 10*Contribution Points*.*PS*: The participation score for each member. Calculated as $PS_n = PS_{n-1} \cdot \overrightarrow P$, where $PS_{\tiny 0} = 100$, to simulate cumulative growth based on consistent over-performance.*iCL*: The fraction of the total commitment level attributed to each member. Here calculated as $fiCL = iCL \times \displaystyle\frac {1}{TCM \times \overline{iCL}}$ This way we’d set up one single average iCL ( $\overline {iCL}$) for the entire community, instead of generating millions of individual*iCL*s for each member.

#### 5. Results

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