Sybil-resilient conductance-based community growth

Preventing fake or duplicate e-identities (aka sybils) from joining an e-community may be crucial to its survival, especially if it utilizes a consensus protocol among its members or employs democratic governance, where sybils can undermine consensus, tilt decisions, or even take over. Here, we explore the use of a trust graph of identities, with trust edges representing trust among identity owners, to allow a community to grow without increasing its sybil penetration. Since identities are admitted to the e-community based on their trust by existing e-community members, corrupt identities, which may trust sybils, also pose a threat to the e-community. Sybils and their corrupt perpetrators are together referred to as Byzantines, and our overarching aim is to limit their penetration into an e-community. Our key tool in achieving this is graph conductance, and our key assumption is that honest people are averse to corrupt ones and tend to distrust them. Of particular interest is keeping the fraction of Byzantines below one third, as it would allow the use of Byzantine Agreement (see Lamport et al. The Byzantine generals problem, ACM Transactions on Programming Languages and Systems, 4(3):382–401, 1982) for consensus as well as for sybil-resilient social choice (see Shahaf et al., Sybil-resilient reality-aware social choice, arXiv preprint arXiv:1807.11105, 2019). We consider sequences of incrementally growing trust graphs and show that, under our key assumption and additional requirements, including keeping the conductance of the community trust graph sufficiently high, a community may grow safely.