Belief-Based Behavioral Diffusion and the Limits of Incentive Design: Interpretability as a Structural Constraint

Abstract

This paper develops a dynamic framework for behavior-based belief diffusion in networked environments, where individuals choose whether to support, reject, or ignore content according to a softmax utility based on evolving private beliefs, plat- form incentives, and alignment with institutional goals. Crucially, belief updates occur through localized social learning, but are filtered by a potentially distorted inference process—mapping observed behavior to inferred beliefs—which evolves recursively over time. We show that such endogenous filtering distortion can accumulate, leading to structural irreversibility in belief dynamics and a collapse of effective incentive reach (EIR). Leveraging tools from dynamic programming and control theory, we derive optimal incentive trajectories that internalize both strategic constraints and interpretability feedback. Our theoretical results characterize the structure of viable incentive paths and identify necessary conditions for long-run belief convergence. Simulations demonstrate that only mechanisms which maintain interpretive coherence—via structural compression, belief anchoring, and recursive repair—can sustain robust control. In contrast, exposure-only or delayed strategies result in irreversible collapse due to epistemic misalignment. Our framework establishes interpretability not as a refinement, but as a structural prerequisite for influence and robust mechanism design in decentralized systems.