A Self-Policing Network

Central nodes with high EC rankings, which have built trust through honest transactions, are unlikely to transact with fake nodes that are not performing real services. Malicious nodes create "island graphs" in an attempt to increase their relative centrality rank within the network. These island graphs will not be able to submit proofs or evidence of their services. As a result, when the network conducts random sampling and slashing, the malicious nodes are penalized with an inverse doping vector, decreasing their EC ranking.

The inverse doping vector, denoted as $\vec{d}$, is applied to the EC calculation as follows:

where $\mathbf{x}$ is the eigenvector, $\mathbf{A}$ is the adjacency matrix, and $\lambda_{\ ext{max}}$ is the largest eigenvalue. The inverse doping vector $\vec{d}$ has positive entries corresponding to the penalized nodes, effectively reducing their EC scores.

As a consequence, real users learn to avoid transacting with malicious nodes, as connecting with them would lead to a decrease in their own EC ranking. This creates a self-reinforcing cycle where honest nodes maintain high EC rankings and continue to transact with each other, while malicious nodes struggle to gain influence and attract transactions.

The self-policing nature of the network not only maintains security but also reduces the costs associated with identifying malicious actors. By leveraging the properties of the EC rankings, the network creates a sort of Panopticon effect, where the possibility of being caught and penalized discourages malicious behavior.

In summary, the self-policing mechanism in the Local Protocol network emerges from the interplay between the EC ranking system, random sampling and slashing, and the behavior of honest, high-influence nodes. This decentralized approach to maintaining network integrity allows the system to scale securely without relying on costly proofs for every transaction.