PS Simulations

Tests & Simulations - trust but verify

1. Stress factors [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

1. 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.

2. 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.

3. 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 iCLs for each member.

5. Results

Tab. 1 successfully shows that the PS of the three members grows steadily, without spikes, and without being influenced by the size of the community or the changes in iCL (as long as the $\overrightarrow P$ remains constant).