The Convention Gap: Towards Measuring Implicit Communication in Cooperative AI Evaluation

Human-AI teams fail to outperform their best member in 70% of studies, yet no theory specifies when complementarity is achievable. We derive tight bounds for the broad class of confidence-based aggregation rules by integrating signal detection theory with information-theoretic analysis, yielding four results: (1) a complementarity theorem (teams outperform individuals iff error correlation $ρ_{HM} < ρ^*$, with $ρ^* \approx a$ in the symmetric near-chance regime); (2) minimax bounds showing gains scale as $Θ(\sqrt{Δd})$ with metacognitive sensitivity difference; (3) an impossibility result proving no confidence-based aggregation rule achieves complementarity when $ρ_{HM} \geq ρ^*$; and (4) multi-class generalization $ρ^*_K \approx ρ^*/\sqrt{K-1}$. Predictions match observed team accuracy ($R = 0.94$ on ImageNet-16H, $R = 0.91$ on CIFAR-10H) and the multi-class threshold scaling holds on human data ($R = 0.93$, $K = 16$), with robustness under non-Gaussian distributions. The framework explains why complementarity is rare and provides actionable design formulas; results apply to aggregation, not to interactive deliberation that generates novel answers.

Collaborative dialogue can end with apparent agreement while participants still differ on goals, assumptions, or execution plans, creating an \textbf{illusion of alignment (IoA)}. A real-user study across 18 meetings confirms that IoA arises routinely in human collaboration. Yet IoA poses a paradox: if participants were aware of such disagreements, they would already be explicit; if not, they cannot articulate them when asked, leaving IoA invisible to both participants and observers. In this work, we make IoA detectable by generating diagnostic multiple-choice questions whose divergent answers across participants provide direct behavioral evidence of hidden disagreement. We construct \textbf{IoA-Suite}, a dataset and evaluation protocol for detecting hidden disagreement, spanning five task types and six domains. We find that even the best model attains only 49.5% F1, with the bottleneck traced to private context that the dialogue does not surface. We then train \textbf{IoA-Prober-8B} based on IoA-Suite, reaching 51.8% F1 on IoA-Suite. Across the aforementioned 18 real meetings, it surfaces 2.89 hidden disagreements per meeting that participants confirm they had not voiced, transferring to live human dialogue. Further, in multi-agent collaboration, pairing IoA-Prober-8B with LLM agents improves downstream task performance on BigCodeBench-Hard and HiddenBench.

Complementarity is the case in which a human--AI interaction (HAI) outperforms the best prediction benchmark available among its members. Although this idea is central in HAI research, formal work on complementarity remains limited. Existing frameworks do not model how agents' predictions compose into workflow-sensitive multi-agent protocols. We close this gap by introducing a tree-based formalization of complementarity in multi-agent HAI. An HAI protocol is represented by an ordered agent-role configuration together with a rooted planar binary tree whose leaves are decorated by prediction vectors. A local binary composition rule is evaluated recursively along the tree, yielding a tree-relative complementarity functional relative to a pointwise-min oracle benchmark. We prove four results. First, selector-based HAIs, including self- or AI-reliance, cannot achieve complementarity regardless of task, loss, or prediction quality. Second, in regression under squared loss, complementarity is equivalent to Euclidean distance minimization from the ground-truth vector; for $N=2$, the optimal linear-pooling weight has a closed form and a residual-correction interpretation. Third, under linear local composition, every protocol tree defines a barycentric coordinate chart on the simplex of leaf weights; Tamari-cover reparameterizations of protocol trees preserve complementarity, and for $N=4$, they satisfy the pentagon identity. Fourth, in binary classification, no internal local composition can achieve complementarity under endpoint-monotone losses, including standard Bregman and many finite Bernoulli $f$-divergence losses; an analogous obstruction holds for multiclass aggregation under cross-entropy. In summary, our framework shows that complementarity is attainable in multi-agent regression, but obstructed in classification under natural conditions on local aggregation and loss functions.