Formulas for Prestige

General Formula for Prestige

From these assumptions, we derived a generalized formula for the Prestige of a decentralized community:

$$\displaystyle \mathfrak P_{n} = \mathfrak P_{n-1} \cdot \sum_1^i \Delta K$$

Where:

• $\mathfrak {P}_{\tiny n}$ is the Prestige of a community in the given period.

• $\mathfrak {P}_{\tiny (n-1)}$ is the Prestige of a community in the previous period.

• $\Delta K$ is the rate of change of each individual parameter, between the current and the previous intervals.

Calculating K & ΔK

ΔK is the rate of change of individual parameters - to calculate the total change across all parameters, we can simply use the sum of all $\Delta K$, calculated as $\displaystyle \sum_1^i \Delta K_{i}$.

Where the individual parametric change is calculated as:

$\displaystyle \Delta K_{i} = \frac {K_{i_{( n)}}} {K_{i_{( n-1)}}}$

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This change rate is determined by the difference in Key Performance Indicators (the parameters) between periods, each one individually normalized and weighted according to their importance in each Hub using Archetypes.

$K_{i}$ is the product of each individual parameter multiplied by its custom weight:

$K_{i} = w \times p'$

where:

• w: the weight assigned to each individual parameter (p)

• p': normalized-p, calculated as $p' = \frac {p} {p_{(max)}}$

• p: the "parameter" of reference.

Deep-dive: Current Parameters

The system currently uses 5 parameters to calculate a Hub's Prestige and their ability to deliver on operational and business drivers.

Current parameters are:

1. $\overlinesegment S$ (Size) -> $\displaystyle \frac {TCM_{\tt h\cdot}}{max(TCM)}$ A relative value that compares the TCM (Total Community Members) of a Hub against the TCM of the biggest Hub in the ecosystem.

2. $\overline {PS}$ (Average Member Participation), calculated as: $\displaystyle \sum_{j = 1}^n PS_{j} \times \frac {1}{TCM}$

3. $\overline {iCL}$ (Average Commitment Level in a Hub), calculated as: $\displaystyle \sum_{j =1}^n iCL_{j} \times \frac {1} {TCM}$

4. $\overrightarrow P$ (Community Performance), calculated as: $\displaystyle \sum_{j = 1}^n GCp_{j} \times \frac {1} {TCp}$ Given Contributions (from Hub's Participants) over Total Contribution Points.

5. $\check G$ (Growth of Community), calculated as: $\displaystyle \frac {TCM_{T_{n}} - TCM_{T_{n-1}}}{TCM_{T_{n-1}}}$

Normalization of p

Normalized-p is calculated through:

$$\displaystyle p' = \frac {p} {p_{ max}}$$

It uses the highest value of a specific parameter across all Hubs measured during the given period. The weights for the different Parameters (below) can be set by the individual Hubs - and are set by our Hub for the edge limits.

In total, the sum of the weights must always be equal to 100 - in alignment with the models used for Discrete Commitment and Reputation staking in the Āutonomy Matrix.

The Prestige of a Hub, at the current period ( $\mathfrak P_{\tiny n}$), is updated by multiplying the change rate (ΔK) to the previous period's Prestige ($\mathfrak{P}_{\tiny (n-1)}$).