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=TCPGC = TCP.

This situation could be due to two factors:

Factor a.

The Member whose GC=TCPGC = 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 [h][\tt h \cdot], and TCM[h]=1TCM_{[\tt h \cdot]} = 1, then the Participation Score of j in that Period will be calculated as:

PSn=PS(n1)PS_{\tiny n} = PS_{\tiny (n-1)}

meaning that their PS remains constant.

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

Factor b.

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

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

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

Another simple extension in this case:

if PSn>c×PS(n1)PS_{ n} > c \times PS_{(n-1)}, then -> PSn=c×PSn1PS_{n}' = c \times PS_{n-1},

that we can render as:

PSn=min(PSn, c×PS(n1))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 ( pp_{\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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