Evaluation of Delegation-Chain Collusion Attacks on Liquid Democracy Voting for Computer Agriculture Cooperatives Under Quorum Thresholds: An Artificial Intelligence bribery-Resistance Bound for Participatory Governance

Liquid democracy lets members of computer agriculture cooperatives vote directly or delegate their weight to trusted peers, and it is increasingly proposed as a governance layer for participatory decisions on shared machinery, water and data. The delegation graph that makes this flexibility possible also creates a vulnerability that direct voting does not have: a colluding coalition can purchase delegations along a chain and concentrate voting weight without ever buying a single vote on the floor. the present analysis treats that vulnerability formally. It models a cooperative as a delegation graph with a quorum threshold, defines a delegation-chain collusion attack as a coalition that acquires consecutive delegations to route weight toward a target proposal, and derives a bribery-resistance bound that states the maximum share of the electorate a coalition must control before the quorum threshold can be met by purchased delegation alone. The bound is expressed in the coalition's size, the depth of the delegation chain, the quorum threshold and the cost of acquiring a delegation relative to the cost of acquiring a direct vote. Quorum thresholds interact non-monotonically with resistance: raising the quorum can either harden or soften the cooperative against chain collusion depending on whether the threshold is met by participation or by concentration.