2. Cannibal Members

“Cannibal” member + c + PS’

This is an edge-case where we consider what happens if a Member completes all or the majority of TCP (Total Contribution Points) available in a Hub in a period T.

Meaning that for Member j -> $GC = TCP$.

This situation could be due to two factors:

Factor a.

The Member whose $GC = TCP$ is the only Member in the community in a given Period.

In this case we should include a new condition:

if j is a Member of $[\tt h \cdot]$, and $TCM_{[\tt h \cdot]} = 1$, then the Participation Score of j in that Period will be calculated as:

$$PS_{\tiny n} = PS_{\tiny (n-1)}$$

meaning that their PS remains constant.

Else, we can use the general formula for $PS_{\tiny n}$.

Factor b.

The Member whose $GC = TCP$ may be trying to collude, therefore, we need to limit their $PS_{\tiny n}$’s exponential growth.

We do so by introducing a constraint factor (c) that controls the growth of $PS_{\tiny n}$.

Together with c, we will introduce a step of normalization ( $PS_{ n}'$ )- that will protect the Hub in case a collusion attempt.

Another simple extension in this case:

if $PS_{ n} > c \times PS_{(n-1)}$, then -> $PS_{n}' = c \times PS_{n-1}$,

that we can render as:

$$PS_{ n}' = min(PS_{n}, \text { }c \times PS_{(n-1)})$$

The value of c is initially set to 1.4 (40% growth) - later the Hub itself will be able to customize it internally, in the same fashion of the approach with p-minus ( $p_{\tiny \ominus}$ ).

This approach ensures that the growth of PS is constrained by the factor c, and any calculated PS exceeding this constraint will be normalized through the allowed maximum.