What Do You Think I Think? Accounting for Human Beliefs Using Second-Order Theory of Mind

Comparative feedback, asking people which of two behaviors they prefer, has become a standard way to align robot and agent behavior with human intent when the reward itself cannot be specified directly. Preference-based reward learning typically casts the human teacher as a passive oracle answering learner-generated queries. We argue this forfeits the teacher's defining advantage: knowledge of the objective. A teacher who knows the target can construct training examples more efficiently than any learner-driven acquisition strategy, an advantage that widens as the reward's feature dimension grows. However, exploiting this advantage requires an accurate model of what the learner currently knows. We therefore recast preference learning as a human-autonomy team problem coupling two behavioral models: the teacher maintains a model of the learner to design an informative curriculum, and the learner maintains a second-order model of the teacher's model, emitting structured preference constraints (understanding statements) that keep the teacher's model of the learner synchronized. In simulation, an informed teacher outperforms learner-led selection; teacher-model drift under alternating teachers erodes this advantage; and understanding statements repair it, with second-order (ToM-2) statements outperforming mean-belief statements when the teacher's error about the learner is concentrated in a particular direction rather than spread evenly.

Inferring others' beliefs requires more than reading surface signals; it requires tracking who told them what, in what order, and how credibly. The Theory of Mind Utility (ToM-U) formalizes this epistemic state inference problem at the computational level of analysis, specifying what mentalizing computes and why without commitment to algorithmic or neural implementation. ToM-U achieves this by constructing Local Epistemic World Models (LEWMs) -- directed typed graphs that represent agents, state nodes, and the epistemic relationships among them -- and evaluating discrete candidate LEWMs against observed behavior until one achieves sufficient confidence. Five formal definitions specify the LEWM structure, agent node properties including ordered information access history, a bounded proliferation mechanism for recursive mentalizing, three inference procedures, and a residue function that captures the structured trace left by failed mentalizing attempts. ToM-U differs from Bayesian Theory of Mind and adjacent formal accounts, which presuppose rather than derive belief states, and from simulation theory and theory-theory, which lack a formal apparatus for epistemic state inference. The architecture generates directional, falsifiable predictions about mentalizing failure that follow from structural properties of the model rather than auxiliary assumptions, and positions ToM-U as a domain-agnostic mechanism upstream of goal inference and other downstream social cognitive processes.

Productive dialogue alignment requires distinguishing \emph{surface coordination} (acknowledgments and smooth task progression) from \emph{epistemic alignment} (convergence of belief states); standard preference-based methods typically optimize response-level preferences without explicitly modeling the latter. We operationalize Theory-of-Mind (ToM) inference as a control signal within Frictive Policy Optimization by extracting, at each referring expression, a four-part belief structure: the speaker's intended referent, the addressee's interpretation, and each participant's model of the other's belief. This makes friction mechanically computable from epistemic-state comparisons, capturing \emph{silent divergence}, where both participants proceed confidently while grounding to different referents. We evaluate the signal at two levels. At the representation level, ablating the second-order channel reduces misunderstanding recall from $65\%$ to $26\%$. At the policy level, reward-shaping (FAR) and trust-region (FTR) variants improve intervention F1 and warranted-context calibration over DPO, with Brier scores independently supporting the calibration gains. Across three training runs, FAR and FTR remain substantially more stable, whereas DPO varies widely and can degrade intervention competence already present in the base policy. Thus, ToM-grounded friction provides a trainable signal for context-sensitive intervention under referential belief divergence.