Critical Phase Transitions in Bias of MAS: From Individual Thresholds to Collective Cascades

Multi-agent systems (MAS) may amplify individual biases through collective interaction. Although previous studies have documented this phenomenon, quantitative analyses of how system bias responds to varying levels of individual bias, and whether critical points can be calculated in advance, remain limited. Using the bias injection level as a control parameter, we conduct experiments with five models to examine how six network topologies influence collective behavior: ring, sparse random, moderately connected random, fully connected, clustered dual-community, and star. The experiments use different levels of persona prompts as anchors, supplemented by numerical stance injection to refine the parameter grid, and compare publicly expressed and privately reported stances using anonymous private probes. Individual responses to opposing views exhibit threshold-based conformity, with model-dependent switching thresholds $\theta$ ranging from 0.48 to 0.63. In homogeneous groups, the consensus probability jumps from 0 to 1 at an injection level of approximately 0.27. This critical value can be calculated in advance from the dose-response curve and drift rate using the dose-drift crossing law. In mixed groups, the critical fraction of randomly placed biased agents required to trigger a global cascade is approximately 0.44, and varies by approximately 0.3 across spatial layouts. In opposing camps, the collective state shifts between compromise and polarization as topology density varies. These results characterize critical phase transitions in bias from individual thresholds to collective cascades and provide a testable procedure for predicting critical points in advance.