Calculating EC and other dependent & independent params

EC is the most important parameter in the Āut's Participation framework.

It determines the expected contributions of a contributor of a Hub during a specific period.

It’s based on the Commitment Level chosen by the Individual Member, and it’s necessary to determine the ratio between the promise / commitment of a contributor, and their actual participation.

It’s calculated as:

$EC = fiCL \times TCP$

where:

• TCP: Total Contributions Points in a Community. Sum of all contributions points available in a community in a given period. They can be acquired by members by completing tasks and interactions. Each Task and Interaction has a custom weight (spacing between 1 and 10).

• fiCL: Fractional Commitment Level per Individual

---

Deep-dive: Fractional Commitment Level

The Fractional Commitment Level is the iCL of a Hub’s participant (j) in relation to the total.

It is calculated as $fiCL_{j} = \frac{iCL_{j}}{iCL_{tot}}$ where $iCL_{ tot}$ is the sum of all Participants’ iCL, calculated as the ratio between and individual’s commitment level, and the sum of all the commitment levels of all Participants to a Hub in a given period:

$fiCL = \frac{iCL}{iCL_{tot}}$

with:

• $iCL_{j}$: individual Commitment Level of j

• $tiCL$: sum of all iCLs of participants in the Hub $[\tt h \cdot]$: $tiCL = \sum iCL_{[\tt h \cdot]}$

---

EC’ = normalized EC accounting the time factor ΔT

We may consider a time factor ($tf$ or $\Delta{T}$) to determine EC based on the time left in a period:

$$EC' = EC \times \Delta(T)$$

where:

• $\Delta{T} \text{ is calculated as }= \frac {T_{l}} {T_{i}}$

• $T_{l} \text { is the time left in a period } T$;

• $T_{i} \text{ is the total time at the start of the period }T$;

This way it's possible to create a generalized abstraction to factor in participants who join a community after the start of the period T.

This works simply by accounting all absolute time available in a community in relation to each individual member:

$\sum (\Delta_{T}) = \frac {\sum (T_{l})} {\sum (T_{i})}$, from which we extrapolate a fractional $\Delta{T} \text{ as }\rightarrow(\frac {fT_{l}} {fT_{i}}) \times T$

This allows for a continuous calculation of EC for all members in different, arbitrarily small intervals within the same period T.