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.