Lower hypergeometric distribution to increase disconnected nodes tolerence

[Neylix]

Is your feature request related to a problem?

To reach a certain percentage of security, the hypergeometric distribution calculate the minimum number of node that needs to validate a transaction among the total number of nodes in the network.
The ARCH consensus require an atomic commitment of this number of node to validate a transaction, but when the network contains a low number of node, the consensus may be never reach if some nodes are flagged as available while they are not (for internet outage for example).

With 50 nodes in the network the HD calculate a minimum of 48 nodes to validate the transactions. This means the network could have a maximum of 2 non working nodes which is not enough fault tolerant to ensure a stable network.

Describe the solution you'd like

To allow some nodes to be disconnected and still validate transactions in the network, we could add an overbooking of nodes in the elections of validation nodes. But this overbooking should not be part of the minimum node required by the HD calculation. This means the HD should lower the number of required nodes to allow the number of overbooked nodes.
For example if we add 25% of overbooked node with 50 nodes in the network:

• HD requires 48 nodes so 48 + (0.25*48) = 48 + 12 = 60 nodes which is over the nb of nodes in the networks
• HD needs to lower the nb of nodes to 40 nodes so 40 + (0.25 * 40) = 40 + 10 = 50 which can be handled by the network.

When the number of node increase the lowering will not be needed anymore as the overbooking could be handled by the network without lowering the HD.
With a network of 10 000 node, HD requires 195 nodes so 195 + (195*0.25) = 195 + 49 = 244 which can be handled by the network.

Additional context

This issue is an adaptation of the AEIP-26

Epic

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