# 2. Cannibal Members

### “Cannibal” member + *c* + PS’

*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:

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:

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.

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