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

    • Changing iCLiCL: Each member (M[1,2,3]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[1],M[2],M[3]M_{\tiny [1]}, M_{\tiny[ 2]}, M_{\tiny [3]} )

  • a stable performance ( P=GCpECp\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.

  • iCL\overline{iCL} (Average Individual Commitment Level): The average commitment level of all members in the community for each period.

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

  • fiCLfiCL (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=fiCLTCpECp = fiCL \cdot TCp.

  • GCp (Given Contribution Points): The actual number of contribution points contributed by each member, calculated as GC=PECGC = \overrightarrow P \cdot EC.

  • PS (Participation Score): The cumulative participation score for each member, calculated as PSn=PSn1PPS_n = PS_{n-1} \cdot \overrightarrow P, with PS0=100PS_{\tiny 0} = 100.

4. Approximations for convenience

  1. TCP: The total contribution points available in each period. Here we constrained using the formula TCPTCM100TCP \le TCM \cdot 100 "heavy tasks” worth 10 Contribution Points.

  2. PS: The participation score for each member. Calculated as PSn=PSn1PPS_n = PS_{n-1} \cdot \overrightarrow P, where PS0=100PS_{\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×1TCM×iCLfiCL = iCL \times \displaystyle\frac {1}{TCM \times \overline{iCL}} This way we’d set up one single average iCL ( iCL\overline {iCL}) for the entire community, instead of generating millions of individual iCLs for each member.

5. Results

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